In answer to your original question OP I would like to say that I handle it very well but unfortunately I don't particularly.

I let it go, and slide off me best I can, in the knowledge it's almost always about them and their issues not me. It happens a fair bit where I work, sarcasm/insults are a common form of communication. It's called 'banter' I suppose.

It isn't at all my style, my humour is gentler and I'm fairly literal so it doesn't sit well with me.

Officially the work company handbook says banter is banned from the workplace but in practice it happens all the time.

It stresses me a little but I keep quiet and get on with my work. I then shrug it off best I can. Realistically I can't stop it, only control my own reaction.

Not sure if any of this is helpful but it's my experience.