Natural selection does not remove mutations. Natural selection is just that if a species survives to reproduce their genes get passed on. I am not sure what you mean by mutations have a hard time surviving in the gene pool. No mutations add new genetic information and most mutations do not affect the organism in any way. I already explained natural selection and hopefully now you see why your question about knowing mutations is just silly. I could not possibly show you how many beneficial mutations there are because a mutation that is harmful or silent in one environment is the same mutation that allows an organism to survive in another. Mutations rarely pop up that are just beneficial in the environment the organism is living in.
Geneticist R.H. Byles say's the first condition that has to be met for mutation fixation is a naturtal enviornment.
Natural selection must be inconsequential at the locus or loci under investigation. This is because natural selection tends to work against fixation of mutations in other words, it tends to prevent their becoming a permanent part of the gene pool of a population. Natural selection keeps things stable rather than helping them to change. B. Clarke points out that even so called advantageous mutations are harmful in that, because of increased competition, they can reduce population size, making their fixation nearly impossible. He adds that they will almost certainly lead to extinction of the mutant gene or organism, and possibly even the entire population.
The effect of Byles's first condition is that the environment must be selectively neutral, or else the mutant gene will never be retained in the population, preventing even slight change. But according to J.T. Giesel, most locations are almost certainly not selectively neutral. Thus, in the vast majority of cases, Byles's first condition will not be met.