It's not an expression I've heard much but the man is basically saying to keep his money

He doesn't want the other person's money, and is somehow offended by the offer of money. So he's being quite insulting to the other person. It's short for Stick (i.e. put) money up your . . . you can imagine the rest, especially if you've ever had a colonoscopy. This is an expression in English, though it's more common with 'shove' than 'stick'. As I said, it's vulgar and instulting, so don't start using it in class or job interview . . . and maybe not at all.