To slag someone off is to chat absolute rubbish about them, usually when they are not there to clap back. It is basically bad-mouthing with a proper British flavour, from petty moaning to full-on character assassination. Can be jokey in a matey way, but it often carries a nasty edge, so tread carefully.
"I nipped to the loo and came back to Dave slagging me off to the whole table, saying I dress like a lost PE teacher. Cheeky sod, he shops at Asda in sliders."