What you're considering is actually a field of research called genetic programming. A lot of information can be found at http://www.genetic-programming.org/.

In most genetic approaches, three operations are considered: selection, mutation and crossover. They are considered mandatory to fully and efficiently explore the function space. At the moment, you only seem to consider selection and mutation, but not crossover (it's mating two individuals to create offspring with characteristics of both parents).

Anyway, don't get overexcited, there's not many real world applications where GP did a good job.

Just my 2 cents, -gjb-