[PatrickHenry]

On the other hand, the accumulation of enough “detrimental” mutations leads to the extinction of a species. Is this an incorrect statement of the basic premise of evolution?

This part isn't quite right. I don't think any species gradually mutates itself into extinction. Rather, due to environmental changes (climate, predators, whatever), it's unable to survive.

[Lucky Dog]

This part isn't quite right. I don't think any species gradually mutates itself into extinction. Rather, due to environmental changes (climate, predators, whatever), it's unable to survive.

Thank you for the clarification. The first part, then, is correctly summarized?

Let me restate: Perhaps, then, it is the failure of a species to accumulate the requisite number of favorable mutations to resist the negative changes in natural selection pressure that leads to extinction.