I have heard in upanyasam that when Sriman Narayana incarnated as Lord Kirshna, he did so in a transcendental form. In Mahabharata’s Mausalya parva, it is stated that Arjuna performed the last rites for Sri Krishna. Are there any explanations for this?

Perumal is eternally with His transcendental nature, wherever he may be. In this context, it means He always appears with conch and discus. He would have shed His mortal remains for which Arjuna would have performed last rites and had ascended to His abode with His divine form.