Would this shoe be functional in a race...
Would this shoe be functional in a race where there's a combination of running + Swimming + climbing? I'm doing the Tough Mudder and I'm not sure if these will hold up for 13 miles when it may be lots of running up and down hills.
I would say no. These are heavier than what you'd want in a running shoe, swimming with them is only to get from A to B (in a canyon) and there are better climbing/approach shoes that you could run in. These are primarily for canyoneering where you need traction and stability and can make the other sacrifices. Check out this shoe, which has the same (or very similar) traction, but is much lighter and easier on the feet for running. http://www.backcountry.com/five-ten-guide-tennie-approach-shoe-mens