Cut the green parts off and start them in a new pot. Let them callus first (days to weeks to months - I have cut cacti before and let them in the air for weeks to maybe a couple of months - they are that succulent) before sticking in any media (perlite works for rooting) - they are fairly easy to do. Check for scale too. They can overwhelm cacti like this and monstrose types (hiding in crevices that are impossible to get to).

The greying out parts could be scabbing over from edema or sun scald.