Given that evolution its driven by two main factors, gene rate of mutation and the number of available niches in the food chain, so there are two plausible paths:
It's an apocalypse nature has died out too
There's no competition as the ecosystem just has gone into a mass extinction event, no more monkeys, birds, lots of insects and variety of plants, this scenario its just plausible from the first centuries to the first million years mark depending on how radical are the mutations that you talk about, I'll go for the most extreme case, life gets mutated radically almost instantly in a random way, this means that evolution driven processes will happen extremely fast, there would be a whole new ecosystem with new species appearing and getting extinct constantly until certain equilibrium its reached.
Equilibrium has been reached or nature hasn't gone into mass extinction
Physics are physics and there's no way around that fact, eventually nature finds the most optimal way to occupy its niches, for example, ants have virtually perfected their hive lifestyle, for new species to compete with them they would have to had a very specific and very intentional traits as competition would rule them out before they become better than ants, there's a reason also why convergent evolution its a thing, there are some things that there are just not a better way to do them, eyes are a good example of it, there its just no better way to get more information from the ambient, that's why they are so common, so in this scenario the mutation wouldn't be much of a deal, maybe within their respective hot spots it will kill most things but it would go that far, nature would adapt to it pretty quickly, actually there's a place that this exact scenario actually have happened, its Chernobyl and it hasn't changed all that much, there's actually a lot of wildlife there.
So given this facts I would say that the most likely scenario for what you want to happen it would be the first one, but as I said, it would eventually create its own equilibrium where most mutations really don't offer any advantages so the mutated creatures usually just die out, to kill nature its actually a lot harder, it would have to be something like Jame's Corey protomolecule, some weird nanotechnology that uses AI to adapt and repropose matter to its own ends