Sexual reproduction can remove bad mutations. Imagine two parents. One has bad mutations m1. Other has bad mutation m2. They have three children. The first gets only m2. The second gets both and dies. The third inherits neither.
Even though neither parent was fully healthy, one of the children was. Asexual reproduction cannot do this.
No, of course not. But having diploid, paternal and maternal DNA is something you need sexual reproduction for.
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.
Let me rephrase to be more neutral. Imagine two genetic lines. Both lines have one bad mutation. Survivable, but makes the individual less fit. With asexual reproduction evolution has to pick one or the other. With sexual it can get rid of both.
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.
Imagine a flax bush with a mutation that causes smaller leaves and a separate one that makes it live longer. Remember, mutations are completely random. In asexual reproduction it's probably going to be about as prevalent as the wild type (the default without these mutations). In sexual reproduction the repeated shuffling of genes will eventually (quite quickly in this case) produce one with the longer life but without the smaller leaves.
Even though neither parent was fully healthy, one of the children was. Asexual reproduction cannot do this.