The people of Waknuk kill deviations and mutations for two interconnected and mutually supporting reasons, one practical and one religious or ideological.
The practical reason is that they live in an area that still suffers from radioactive contamination from a nuclear war centuries ago and so there is a high mutation rate among plants, animals, and even people. If mutations were not removed from the breeding pool by killing or (in the case of humans) sterilizing and exiling them, it would be all but impossible for living beings to breed true.
But why is it so important that things breed true in any case? Apart from the practical consideration that most mutations weaken their host rather than strengthening it, the people of Waknuk have a religious reason for obsessing over purity of descent in all things. They believe that the nuclear war was a Biblical-style "Tribulation" sent to test humankind with suffering and temptations to sin, and that when God created all things, He gave them an orthodox form that would never vary unless the Devil entered into them to tempt and corrupt human society. Thus, eliminating mutations and deviations is not merely a practical matter -- it is a moral imperative commanded by divine law, one that might well bring on further Tribulation if neglected.