What it means
To slag someone off is to chat nasty about them, usually when they're not there to clap back. It can be a bit of mates taking the piss, but most of the time it's proper running someone down, rinsing their face, their outfit, their job, their whole vibe. If someone says you're getting slagged off, that's not cute and drama's already lacing its boots.
Usage examples
"I popped to the loo and came back to Dave slagging me off to the whole table, saying I dress like a budget PE teacher."
"Half the office was in the lift slagging off the new manager and the doors opened on the new manager. Proper Eastenders moment."
"Don't bother going to that pub on a Sunday, the regulars spend the whole roast slagging off the away team and anyone wearing the wrong shirt."
"She smiled through the whole meeting, then went straight outside and started slagging me off by the bike racks."
"They were all in the group chat slagging him off for wearing loafers to the pub, absolute savage little corner of the internet."
Where it comes from
It comes from slag, the waste left over after smelting metal. That word was already in English for centuries before it turned into an insult. By the early 1900s slag was being used abusively, and slag off settled into British slang around the mid 20th century for laying into someone with scorn.