I perfectly cleaned up my room about two years ago, so there are not anyis nothing that I just don't have the heart to throw away.

"not anything" can be simplified to "is nothing". and "are' doesnt come before "anything", "is" does.

That's grandfather's memento, and it's very cool.

I perfectly cleantidied up my room about two years ago, so there are not anything that I just don't have the heart to throw away.

We would say "perfectly tided" or "completely cleaned". But we don't say "perfectly cleaned. This is because "tidying" refers specifically to placing things in their correct place and cleaning is something that includes removing germs/dust/particles.

On the other hand, I have thHowever, I keep one keepsake I definitely don't want to throw away.

That's memento from my grandfather's memento and it's very cool.

I perfectly cleaned up my room about two years ago, so there are not anything that I just don't have the heart to throw anything away.

Lots of ways to phrase this. Just be careful of double negatives and use contractions.

On the other hand, I have theis keepsake I definitely don't want to throw away.

Leather grloves. (?)

That'sey are my grandfather's memento and it's very cool.

I perfectly cleaned up my room thoroughly about two years ago, so there are noisn't anything here that I just don't have the heart to throw away.

I didn't correct it, but "I just don't have the heart to throw away" sounds a bit strange here. Maybe "Iyou don't want to throw away" is better.
Also, "perfectly" (I guess you mean 完璧に or 完全に) is not quite right here. Thoroughly 徹底的にmay fit better.

On the other handHowever, I have thea keepsake I definitely don't want to throw away.

"On the other hand" is better used for total opposite things/situations. However is ’しかし or だが and flows better.

Leather grloves.

Better would be "a pair of leather gloves".

That'sey are a memento from my grandfather's memento and it'sare very cool.

Gloves is plural.

I perfectly cleaned up my room about two years ago, perfectly....¶
so there areis not anything that I just don't(want / have the heart) to throw away.

adverb after the subject is more natural here.
are is used for pronouns like you, we and they.
The double negatives at the end make it a bit confusing, keep it simple.

On the other hand, I do have thea keepsake I definitely don't want to throw away.

"a" should be used here since you didn't specify a specific keepsake yet.

Leather grloves.

That's my grandfather's memento and it's very cool.

adding "my" here makes the sentence more complete and sound more mature. If you're writing in the perspective of a child /teen it could work.