The sentence, as you have written it, is grammatical. If you are referring to your clothes (and nobody else’s clothes). However, if there are context clues in the text drawing the reader’s attention to the fact that you are throwing your clothes on the floor, it would be a bit more elegant to use ‘the’.
My or me are both grammatical alternatives. Me might sound a bit less formal, but is still correct.
For language proficiency tests, in English class, and in formal writing and letters, my is required here. It is the throwing of clothes that is not minded, not the person him/herself. The first two sentences below refer to a personal hate; the third refers only to a strong dislike of the clothes-throwing:
He hates me.
He hates me (when I am) throwing clothes.
He hates my throwing clothes.
.
“You” is often used in informal English, but it is grammatically incorrect.
My comment about “the”:
Using “the” indicates that you’re speaking about ‘specific clothes’. (Probably specifically mentioned in an earlier sentence.)
Without using “the”, then it would mean ‘clothes in general/anybody’s clothes’.
Yes, you can say “my clothes”: He hates my throwing my clothes on the floor.
But, some people might prefer not to have “my” twice in that sentence so close together and, for style reasons, might decide to word the sentence differently.