He treats me like his slave.

Literal

He [topic-は] me [object-を] his [genitive-の] slave [like-のように] treats.

~のように ('like, as if') attaches to a noun to draw a comparison or simile. The whole phrase 彼の奴隷のように modifies 扱う ('treat') adverbially: 'in the manner of his slave.' The polite ます-form 扱います suggests this is being said to someone outside the speaker's immediate circle — perhaps as a complaint or grievance, where the politeness paradoxically heightens the indignation by keeping the language formal even while describing mistreatment.