If the mutations are random then the biological viability/fitness would also be random.
This is true as far as it goes. If we assume that a population of genetically identical individuals of equal fitness gives rise to a new generation who differ only due to random mutations then the distriution of fitness in the next generation will reflect the randomness of the causative mutations.
The 'non-randomness' of natural selection is principally just some obvious observations on the repercussions of certain types of mutation. Mutations which prevent the embryo from developing will not be passed on to the next generation, mutations causing sterility will not be passed on to the next generation, mutations which lead to an individual having more offspring will tend to be over represented in the next generation, mutations which lead to an individual having less offspring will tend to be under represented in the next generation.
So while the initial distribution and effect of the mutations is random the set of mutations passed on to the subsequent generation and their frequency is dependent on the interaction of each particular mutation with its environment. Assuming no further mutations occur in the next generation the frequencies of mutations in the subsequent generation will not reflect the random distribution of the mutations in the previous generation.
The whole system is only random to the extent that it has some random element in it.
TTFN,
WK