I'm not sure about that. Mutation is a random process,

The problem is entropy. You keep modifying parts of a machine and eventually it'll break. It is infinitely harder to keeps things working based on random changes than for it to break. It's like picking a random car part from a store and shoving it in your car regardless of make or model. The chance that it won't work is the majority. Unless something is necessary for an organisms survival, it is at risk of breaking. After that, the chance it will be fixed by another mutation is nil.

and natural selection is pretty random as well.

No it is not. It's imperfect but if natural selection was random then evolution would be a farce.