This is a common misconception. As AndrewL indicated, most mutations are totally neutral with regards to the survival of the oraganism. If, instead of mutation, you meant “mutation that results in a new phenotype that has some impact on survival,” I’d agree with you.
you look alot like your dad, if your dad didn’t die before you were born then there are more people in the world that look like your dad, if someone has lots of kids that don’t die then lots of people look like your dad