Biologists themselves say this: Evolution is driven (largely but not wholly) by random mutation acted upon by natural selection. The “random” mutation together with natural selection is not a random process. But it’s not a directed one, either — there is no goal or purpose or telos to the process, which is mindless.
However, as many have noted, even the use of the term “random” with respect to a mutation is unfortunate, producing lots of misconceptions. A better way to put is that a mutation is uncorrelated with the adaptive needs of the organism. This is explained more fully by Stephen Barr, a physicist, an expositor of evolution and (as it happens) a Catholic:
Earlier I posted the example of the evolution of nylon-eating bacteria. The evolution of the ability to digest nylon was uncorrelated with respect to the state of the environment or the adaptive needs of the organism. An similar mutation may have occurred thousands of times in the past in environments wholly lacking nylon; in such cases, the mutation would either have been neutral or deleterious: It would not have affected the organism, or it would have harmed it.In their college-level textbook Modern Genetics, F. J. Ayala and J. A. Kiger explain three senses in which mutations are said to be random: first, as “rare exceptions to the regularity of the process of DNA replication”; second, because “there is no way of knowing whether a given gene will mutate in a particular cell or in a particular generation”; and third, because “[these mutations] are unoriented with respect to adaptation.” They note that this last meaning “is very important for evolution . . . . Mutations occur independently of whether or not they are adaptive in the environments where the organisms live” (emphasis mine). Mutations are produced by various causes, such as natural radiation or genetic copying errors. The adaptive needs of organisms arise from quite different—and independent—causes, such as changes in climate or food supply. This produces a lack of systematic correlation between when mutations happen and when they are needed, so the former are “unoriented” with respect to the latter.
But in the case of the actual evolution of the nylon-eating bacteria, it just so happened that the mutation arose in a population dwelling in waste water filled with nylon. So then the mutation became beneficial.