Organisms can only have bad mutations if they reproduce sexually?
Apart from that, it's also wrong because sexual reproduction did not get rid of anything. Just one offspring not affected, but the premise already established the fitness of partial carriers, so that mutation is gonna remain in the gene pool.
You are not really thinking this through. How would a fitness reducing mutation become a feature of a genetic line in the first place in asexual reproduction? The "silent" partial carrier dynamic of genetic defects is a problem exclusive to sexually reproducing organisms.
How can sexual reproduction "get rid of them"?
Play it out for a few generations, you will see, there is a frequency equilibrium. We've done this in school with paper, but if you know some programming, it's an easy exercise. Anyway, unless being very detrimental for partial carriers, the bad allele is gonna stay in the gene pool.
A random mutation. Especially when combined with the founder effect or some other genetic bottlenecking.