My cats did it all by themselves in my last fortess, is was just a starting ditch/pallistade fortress surrounded by sinister and terrifying marshes. So, beak dogs showed up just outside the 'fort' and as cats are the only pets that dont have the sanity to stay inside the building, they all ran for safety by running out of the fort. Dead cat all over the map. I didnt like it, I needed them for soap, and I my plan to trap the beak dogs (also for soap) also failed.
Even without artificial stupidity, theres plenty of ways to get rid of them. Exploiting their different pathing is probabaly the best way, using flowing water to wash them to their doom keep your dwarves from getting killed by it (most of the time).
For example, use pumps and diagonal flow to make a waterfall with a corridor right before the fall part. Make a corridors dwarves normally wouldnt use, for example, by using traffic zones. Cats will just run about your fort, ignore traffic zones and eventualy take the ill fated corridor, getting washed down the waterfall, into whatever-doom-you-like. (or cage traps, wounded cats will pass out and get caught even if they are a pet).
Never have needed this though. I keep my female cats chained in places where their offspring doesnt have too great a chance to survive. Only made by accident once, it resulted in a rather disturbing pile of annimal corpses at the bottom of a ~10-z-level drop in a majour river.