Do I still need mutation if the sale deed (registry) is already done?

The registry and mutation are two different things and you need both. The registered sale deed transfers the title to you, that is your proof of purchase. Mutation (dakhil kharij) updates the village revenue record so your name appears as the holder. The seller is right that the deed makes you the owner, but he is wrong that mutation is not necessary. Without mutation your name will not be in the khatauni, jamabandi or 7/12, and that creates real problems: you may not get a crop loan or KCC, you cannot easily claim scheme benefits like PM-Kisan that need your name in the record, land revenue notices keep going to the old owner, and a future sale becomes harder. So always complete mutation after registration. Note that mutation is not proof of title, it is proof of possession and record, but it is essential. Confirm the mutation process at your tehsil. This is general information, not legal advice.