How do you mentally cope with your physical pain?

Mind over matter... I don't mind so it don't matter.

That is rather glib, but it DOES work to an extent. We notice what we pay attention to. The more you focus on your pain, the more the pain will draw your focus.

A few months back I was shot in the shoulder at point blank range. It hurt like the Dickens, but I felt the impact (which broke my collarbone) not the rending flesh. I seriously didn't even know it was an actual bullet (I thought it must have been a bean bag round or something like that because of the impact) until my hand came away bloody. The pain almost immediately subsided as I realized I needed to get to a nearby house and have them call 911. And it stayed away while I worked through ensuring the scene was safe, self aid, police report, and notifying my employer. Once I had taken care of my responsibilities and I heard the ambulance coming so I could "surrender" to the injury, the pain got a lot worse real quick.

Once I was in the hospital, the pain was never all that bad as long as I was occupying myself with other things. When I thought about the pain it got worse.

Obviously, we should rarely just ignore pain, and even when we do, we can't ignore it for ever. But finding other things to focus on goes a great way to mentally dealing with the physical pain.

For me, staying busy helps – music, short walks, and sometimes certain cannabis strains like Guava Dawg help ease the pain a bit. If you're curious, you can check it out here:
https://strains.uk/weed-strains/guava-dawg-strain

I find the hardest physical things I can do without making my pain or injury worse…and I do the hell out of them. I try to enjoy what my body can still do.