So I'm trying to make a go kart out of a push mower engine. I weigh 75 lbs, I'm crazy light if you were wondering how I'm so not heavy. Whatever. Anyway, the kart will weigh around 15 lbs, maybe. I am wondering if its possible. The mower has 4.5 horsepower.

Torque is dependent on the radius of the gears you will use. Check this link, it uses a gocart.
https://www.researchgate.net/post/How_can_we_calculate_the_required_torque_to_move_a _massive_object_by_means_of_gear_assembly2

How are you going to build a 15 lb go cart? The wheels and tires will weight that much alone, its not going to be easy to make a 115 lb one (without the engine) Impossible with.

How fast are you trying to go?