Yes, use a bandsaw, coping saw, any saw to rmove lumps of wood first: part of the initial 'big picture' work.
But what about when you are well into your carving?
Well, you can certainly pick up your saw again; I always keep a coping saw handy near the bench. But there are often opportunities to remove 'extra' wood with your carving tools: getting more 'bang for you buck' as they say.
There are 2 techniques I want to give you, what I call, 'trenching' and 'bursting'. Just bear these ways of working in mind as you go along and you might be amazed at how you can speed up getting that wood gone.