You're right about the meaning - it means manage to get to his feet. The basic phrasal verb is 'make it', meaning manage to do something. 'Up off the ground' is a compound adverbial phrase,, up + off somewhere, indicating direction.
It's quite usual to combine 'make it' with adverbial phrases in this way. For example, 'make it to the top' is a very common expression meaning to succeed in getting to the top of something - either something literal, such as a mountain, or figurative, such as a career path. Likewise, a common way of saying, 'I hope we manage to escape from this place' (correct but slightly unnatural) is 'I hope we make it out of here' (very natural).