If you are not happy with the examples I gave you of external mutagens, mutations can occur spontaneously through errors in the replication process.
the concept that "some mutations provide survival advantage"
You are jumping all over the place here. Remember you stated earlier that the evidence is no better for natural law than for "elves". My response was that the observations are in fact in strong agreement with natural law (mutations). At the very least the evidence favors something "unintelligent" doing the design work.
Now you asking how these mutations increase fitness (a seperate question entirely). In plenty of cases it is known why an apparent mutation (i.e. a difference between chimps and man) would be advantageous. In other cases it is not so clear. Nonetheless, there is strong evidence in favor of random mutation.
If I understand your response, it can be boiled down to this:
(1) TOE is dependent upon "natural law" for the cause.
(2) Natural law in this context can be defined to be mutations.
(3) Ergo, mutation drives TOE.
But where is the evidence for this? Since almost all mutations cause negative effects, where is the demonstrated "increased fitness"? Remember, "fitness" is defined as: increased number of offspring, or greater survival ability of offspring, or both. (That's not my definition, that's the accepted definition of fitness which arose, I think, to counter the tautology problem of the "Survival of the Fittest" phrase.)
You are begging the question when you assert: "...it is known why an apparent mutation (i.e. a difference between chimps and man) would be advantageous" since you have not demonstrated that those differences are in fact due to mutation as the causative factor. Your argument here boils down to:
(A) Mutation causes genetic change.
(B) We see differences between similar species.
(C) Therefore, these differences have been caused by mutation.
Again, this is reasoning "by induction". Which is weak. Yes, there is evidence of mutation. But evidence that mutation works to produce "fitter" critters is lacking, I assert. And the whole TOE hangs upon this one point.