No, there is not a saw for that.

Yes, it could be done---however, the raw edge would need shaping/sanding/finishing---and those procedures also do not have tools made for those jobs---so----removing the old and replacing with new is much more inexpensive.

Due to the fact the old baseboard was left in place---the new will not hide the gap left when the old is removed---so quarter round or shoe molding will need to be added to hide the gap.

There's always a way to do something but in this situation I wouldn't imagine it would be easy or inexpensive. There isn't a saw per se. You'd have to make some kind of jig and probably use a router. Even then, there would be a fair amount of handwork.

It would probably be easier to remove the old baseboard. Baseboard usually doesn't have that many nails in the bottom 3/4" or so taken up by the flooring. Since you plan on replacing it with smaller moulding you should plan on some drywall patching and painting.

Mike

There is a saw made by Crain (812H) for trimming door jambs and even doors while still hung. It adjusts up to more than 1 inch high, but can be blocked up even higher.

A jamb saw might work but there would still need to be some kind of rail system for the saw to ride on. Baseboard should be installed level, not parallel to the floor.

In any case there'd be a fair amount of handwork cleaning up the cut and getting into corners.

I still think it would be easier to replace the baseboard.

Mike

Thanks everyone.