Most of the time, if a new floor is going to be installed, a 1/4 inch layer of plywood underlayment is put down over the old floor without worrying about the backing. I don’t know of an easy way to remove the backing. I have heard of people using heat to soften the glue, or using bags of ice to make the glue brittle.

One thing, if the floor you are removing is pre 1977, there are good chances that the backing contains asbestos, so be careful!

Good Luck! (let us know if you find an easy way)