I don't really understand what you mean, could you elaborate? Neither MUST be anything, they are what they are. I don't think there is any proof that things MUST be the way they are for anything in the world (though I could be wrong). Also, there is recent (and controversial, maybe not the best science) evidence for non-random mutation in bacteria, but why does that mean that it MUST be directed by something supernatural?
(
http://www.nature.com/nature/journal/v485/n7396/abs/nature10995.html)
Mutations are random because of how we define the word random...
The mutations that yield the hereditary variations available to natural selection arise at random. Mutations are random or chance events because (i) they are rare exceptions to the fidelity of the process of DNA replication and because (ii) there is no way of knowing which gene will mutate in a particular cell or in a particular individual. However, the meaning of "random" that is most significant for understanding the evolutionary process is (iii) that mutations are unoriented with respect to adaptation; they occur independently of whether or not they are beneficial or harmful to the organisms. Some are beneficial, most are not, and only the beneficial ones become incorporated in the organisms through natural selection.
(Francisco J. Ayala, "Darwin's greatest discovery: Design without designer,"
Proceedings of the National Academy of Sciences USA, 104 (May 15, 2007): 8567-8573.)
Have you asked the PI of an oncology lab on campus what proof for random mutations exist? I would start there, you two could have some great discussions.
Do you mean unguided in the sense that there is no purpose to evolution other than to continue? Meaning humanity is a byproduct, and not placed here by a big dude? Or do you mean unguided in the sense that random phenotypes get passed on at all, because that is "guided" by selective pressures.
Again, my apologies for not comprehending your direction there. FWIW, I agree that God and Evolution can co-exist, but this requires a somewhat unorthodox approach (Non-literal interpretation of the Bible/Quran/Insert old book here)