Why could this not be: The taste of the apples that I cut with the knife is very nice. ... "The knife" instead of "a knife."
It is already accepted :)
If it's not accepted, it's just a forgotten alternative - report it.
When you mistype and forget to put the "a" article.
This sentence seems to implie that because the apples were cut with a knife - or specific knife - it gave them a special taste.
It could be. Or there might be two groups of apples: tasty ones and soury ones for example. I have already cut the good ones, and I am telling you to take the sliced ones because they taste better.
Is there a reason why this has to be 'the apples' and not 'apples'?
Kestiğim elmalar → The apples that I cut. They are the definite apples, because they are the ones that I cut.
If you want to use "apples" as a indefinite noun, you can use "bıçakla kesilen elmalar".