After hundreds of deaths/failures, you mute the game and pass in one try

Getting the Pure Platinum in Chapter 12 of Bayonetta 2 was done in 5-10 tries after muting the music, and I had to have been trying 50+ times at that point.

Otherwise, no. I just do the "put it down for a bit and come back to it" thing. Example: Nioh's last level with
the stupid Kelley clones
OP, out of curiosity, do you use a receiver that sends the sound through external speakers? Sometimes those have delay, and muting the delayed sounds would certainly help you play better.
I do actually, but this is a trick I've been using since I was a kid playing on a CRT monitor, delay free. I haven't noticed a delay or anything with my speaker system, maybe I'll look more closely next time.
This works very well for me too... I used to notice it most with racing games. I would mute and carry a conversation with a friend, or just zone out, and come out much better at the end.
Not in one try, but this helped me beat the dash challenge legit in Hyper Light Drifter. Something about the sound effects just didn't line up with the visual cues and I found myself desyncing - muted the game and boom it became much easier.

And then I found out you can just cheese it with a keyboard and mouse.....oh well.
Bad sound design?

I know with a lot of Nintendo games, the sound is such an intrinsic part of the gameplay that I'm completely lost without it.
Pretty much the only way I can play MLB The Show with out getting pissed off is with commentary off. I wish they didn't bother recording some of the lines which criticize the player for swinging at dumb pitches.

"He'd need a 10ft pole to reach that one - not sure what he was swinging at"

I always mute the music in games, been doing it for as long as I remember. It's hard for me to not focus on/analyze music when it's playing, even if in the background. I also like games for the gameplay, I like to get my music from other, more enjoyable ways.
I’ve done this a fair few times, most recently on The Mile High trophy on COD4 and a couple Nioh bosses. Just really helps you focus on everything in front of you.

Also if there is a bit of unskippable dialogue at the start of each life that adds an extra layer of annoyance before you even get to the actual hard part of the game.... helps with that as well lol
I never mute my games but I remember doing this a couple of times out of anger when I was a kid and it actually worked lol. I didn't remember this at all... Thanks for the memories OP, I was one impatient child.
Bad sound design?

I know with a lot of Nintendo games, the sound is such an intrinsic part of the gameplay that I'm completely lost without it.
I've muted plenty of games with excellent sound design, Nintendo games included. This seemingly leans more calming one's nerves by eliminating extraneous senses after repeated, stressful failure. If anything, I'd say it's actually poor gameplay design to require sound to play a game at all times, since it disregards the different conditions players may need to play their games with, and since leaning into one aspect of design too heavily is imbalanced.

Rhythm and music games excluded of course. And definitely moments where sound cues are your only clue, although this is pretty rare.
Guitar Hero whatever #: Queens Of The Stone Age - No One Knows. Hearing that song is like nails on the chalkboard. I just hate the beat. I tried multiple times beating that song in the game. I tried muted it, and sure enough I was able to get passed it.

Similar, in Dark Souls 3, when you fight Yhorm the Giant and you get The Storm Ruler. I fought the boss a few times, got close. So I tried pumping myself up with the song Let The Storm Descend Upon You, by Avantasia, because of the storm theme. It worked that time!
Yes, but not always for the exact same reason:

- in some rhythm games it's helped me realize there's some kind of slight input delay, so timing my inputs to the music actually hampers me.

- in some non-rhythm games I've realized I am unintentionally timing inputs to the music, and that messes me up.

- sometimes the music ramps up in intensity to the point that it creates a more stressful atmosphere than it actually is, which psychs me out.

And then some cases are similar to what others have said in this thread. When I was trying to tackle a difficult section in Thumper, I'd have to put it aside for a while. If I woke up with the music in my head I knew I'd been subconsciously processing it overnight and would do better when I tried again. If I didn't, I was still stuck at square one.
In Ninja Gaiden on Xbox, Alma kicked my ass so many times I quit the game for like 4 months. I randomly picked it up one day and one shot her, strange.
Kind of the opposite: in college a friend was playing Devil May Cry 3 in the lounge while there was a movie being shown, so he had it on mute. He could not beat a particular boss (vampire lady IIRC). Movie ended, he got to turn the sound on... and facepalmed when he found that said boss had very distinctive audio telegraphs to her attacks. Beat her immediately once the sound was on.
I fucking love that boss because of that. Such great design.

"Are you enjoying yourself?"

"Get ready......sugar."

To answer the OP, yeah I have muted the game to complete a level. I've done it a few times but the last one I did it on was Wipeout HD. It was for that reach Zone 50 trophy while only using the shoulder buttons. The complete silence put me in like a zen state. Crashing in the higher zones also made me nervous so not being able to hear the crash allowed me to mentally recover a lot more quickly.
Had this a few times. Probably has something to do with more focus, due to less sensory distractions.
Happened to me a couple of time most recently on Bloodborne with a boss and an area that I kept dying on. I took my headset off got something to drink then came back and got through the area and boss on the next try lol.
Not with muting the game, but going to bed and coming back to it the next day. Just getting my head out of that space of repeated failure by taking an extended break can work wonders too.
Not going to bed but walking away seems to help me refocus or something. You would think it would throw off timing but it seems to help instead.
Cheap Cheap's cooking stage in Parappa the Rapper HD.
I can bang this level out in a single shot consistently on PSone, even *with* HDTV lag.
The HD port has really fucky input lag/timing (way, way worse off than the PSone version)
I just could not fucking do it. Tried both controller vibrate-to-the-beat options, tried without those, could not do it. Tried on stream 40~50 times.
Muted and just went with the visual flow and beat it first try.
Happened to me in Bloodborne with Ludwig.
The fight has cutscene so I was thinking of letting him kill me just so I could watch the cutscene but decided to finish him off and just watch it from Youtube.
I remember playing Daxter on my PSP many years ago and getting stuck on a boss or something, I then muted the game and was able to get past that part of the game.

I don't really remember if I've done anything like this since then, but I do remember doing this and I was somehow able to concentrate better I guess, or maybe it was just a coincidence?
When i keep failing at something i mute the game and put on some music, i think that helps me to focus. Thats how i did some of the harder stages of crash 1 last week.
Not quite the same, but similar. So on my second run of Dark Souls, I get to Anor Londo, and get all the way to Batman and Robin. At this point, it's about half 1am, so I decide "nah, I'm not going to subject myself to this torture tonight" and go to sleep.

So I wake up after a peaceful sleep, but I'm still groggy. First thing I do is turn my PS3 on, and whilst still in bed half blind from the light of the screen, half aware of the world around me, I proceed to kick their asses first time, earning me Ornstein's soul in the process. That was a victory I was proud of.
Sometimes if I'll get mad at a game I'll lose it and throw my headphones against the wall, 'cause the feeling of the headphones on my head will start to drive me crazy. Accomplishes muting, and yes, it makes me win sometimes.
Not muting, but I'll complain about the level/enemy to a friend and go on about how I'm never going to beat the game because of how dumb that particular part is. Give it another try and what do you know, I get by just fine! Happens every time.