There is nothing "normal" about evolution, unless you include everything in it. Humans are a results of evolution, like any other species. And great extinctions are completely natural.
Great extinctions are "natural" where natural means "part of the universe." There is enormous debate as to which and by how much great extinctions were "natural" where natural means "resulting from the system level dynamics of the ecosystem in question."
Generally mass extinctions weren't directly caused by the actions of one particular species, though…
Except that isn't necessarily true. Wasn't one of the first major extinction events caused by over-oxygenation of the environment?
1. Cyanobacteria aren’t one species and 2. on the whole, oxygenation didn’t work out so well for the anaerobic bacteria that caused it, did it?