The only mites I've ever found on a mantis are what would be considered grain mites. They can't bite you or the mantis. They mainly scavenge food from around the mantid's mouth. Everybody has them but they are generally too small to see so they are only noticed if there is a very bad infestation seen on food left in the tank. I see them all the time when taking extreme macro. That includes on both captive and wild mantids. They all have them to some degree.
Here is a wild Chinese mantis in my back yard. If you look very close you will see some around her mouth and one on her eye. There are five visible in this photo but there were at least ten total on this very healthy wild girl.
And here is a subadult male Oxyopsis gracilis. You can see one to the left on his mouth and two to the right on the eye.
I used this photo as an example because there are more present than I normally see. This is likely due to fact he was close to molt so I was keeping the enclosure extra moist. Mites need a very moist environment so keeping a mantis dry for a couple days usually kills them off. It's also always good to give the container a good cleaning in very hot water right after a molt just to kill them all off. But they'll be back, of course.
They seem to clean up like the small fish that ride around on larger fish. I have never seen a mantis react to their presence in any way. They ignore them completely. I've seen many people freak out upon first discovering them, as I did, but they are harmless. If you use crickets or roaches as feeders you have them. No way around it.
The only time they become an issue is when they infest fruit fly cultures because the fruit flies then must compete for food.
So what you felt bite you was probably just a bot fly, tsetse fly, black widow, brown recluse or a tick with Rocky Mountain spotted fever or Lyme disease.
