Pull or drag would be the best options here. "Tug" means a quick pull which would not fit this context.
Although "draw" can mean "drag," "Drawing someone out" can mean "Encouraging them to be more confident, or to confide in you." so, again, does not fit the context.
"Pull" is the obvious choice, or "drag" if you had to pull rather harder (perhaps he was unconscious). "Draw" is rather a formal or old-fashioned word for the situation, and tug generally suggests a short sharp pull (or a series of short sharp pulls); alternatively it is used for a very strong force indeed.