This has happened to one of mine. A few years ago my female veiled swallowed her tongue for reasons no one understands and it was so damaged by the stomach that it had to be amputated.
She did develop persistent infections in the mouth, despite being put on antibiotics. It was probably due to the degree of trauma and the length of time she suffered through it until I noticed (maybe 16 hours or more) and until someone would see her the next morning.
Had she bitten off the tongue I would have seen it immediately, as I walked past her cage several times. But because she had swallowed it, it was imppossible to see until feeding time. So had I noticed immediately and put her on antibiotics the same day, she probably would have done better.
In the end she died 8 months later, not having really adapted (she never learned to eat on her own, partly due to the discomfort of the infections) But mine is the only sad story I know, I think most people get their chameleons to do really well following an amputation.
And it's not something that happens every day. It's a freak accident usually. Just be careful of their tongue if tong-feeding or whatnot, but there's no need to turn their cage into a padded room.