Sure is, it's called a Toe Kick Saw.
3-3/8" Blade Toe-Kick Saw
Crain makes a better one but if your only doing this one job I'd get this one. Home Depot also rents one. A new Crain is a couple of hundred bucks.
It will cut right to a wall or under a toe kick and not mark it up.
I'd use an Ossilating saw to make the final cuts in the corners where the toe kick can not reach.
A Toe kick uses 2, differant sized blades, one cuts 3/4 deep the other cuts 3/8". The depth is not adjustable. You could lay a piece of 1/4" plywood down under it to lift it up some.
I'd cut that floor in sections with a ciruler saw set to just a little more then 1/4" deep to make it easyer to rip out.