Just ignore him and farm.
Don't bother chasing him in most cases unless you are certain you can kill him with either hard CC or such. Don't bother sending more than just yourself + jungler. Any more than that is the waste of time Singed wants.
Later in teamfights, just have your weakest player that's not absolute garbage at CSing (I don't mean as in their skill, I mean as in how easy it is to CS with said champion at that point in game) show up to the lanes he's trying to splitpush (unless he's trying to double or triple proxy from base) and that should be more than enough.
If he's trying to double or triple proxy, just send one person with a Sweeper to drive him out and check for wards for a TP-return.
The whole point is he's trying to waste your time and make teamfights uneven by forcing you guys to chase him, but if you don't bother, he can't really do much. Also if you just stomp the rest of his team hard enough early on, it'll be hard for him to splitpush well enough to carry his entire team all the way back to victory. Don't just let him get free towers though unless you can get something better out of it.