Actually, I am pretty sure that nowhere in the theory of evolution itself is there any mention of randomness or purposelessness. Those ideas are not scientific. What test would lead you to the belief that the random or purposeless nature of evolution is false? Now individual scientists, on the other hand, often argue precisely that evolution is random or purposeless. If anything, randomness or purposelessness may be assumed on the basis of Occam's Razor. That is, the idea that life evolved as a result of undesigned processes and the idea that life evolved as a result of designed processes are deemed to be equally good at explaining the observations. Occam's Razor tells us not to multiply entities needlessly, so undesigned processes are assumed, since there is then no need for a designer. Science will never accept a designed process since there is no test for it.
DNA mutations are basically "random", and that is the assmption in many versions of Evolution theory as to how radical changes in the genome takes place. Most of these are detrimental, but on occasion the odds come out right to create a superior critter.
I put "random" in quotations because there actually is a significant study of randomness. Genuine "randomness" is a very hard thing to find. And it is sought for, because if you can generate genuinely random events or numbers, you can use them to build very strong encryption codes.
"Purposelessness" is something that I would think is a philosophical issue. Or human phycological issue. About whether God has a purpose for His Evolution creation, or for humans, science can say nothing, pro or con. I think He does, but science cannot tell me this.