I'm used to sculpting and carving (not on the computer) so that's the way I'm trying to approach sculpting in maya (not sure if that's a good idea or not yet).

What I want to be able to do is draw for example a lion. Draw one outline view from the side, one from the top and one from the front and extrude the three views, and have a mesh that results from only the parts where the three overlap, like I have cut it out of a block of foam.
Then be able to edit it further and carve out details and make the body rounded etc.

Is this possible?

If it is could someone please explain how? I don't really know anything about maya yet. Or is this not the way sculpting on the computer works, and should I approach it in a different way?