“Abandoning without residue all desires born of saṅkalpa” — the qualifier is important. What is to be given up is not the body's natural, functional needs but the ego's manufactured wants. Hunger, thirst, breath, the instinct to survive — these are the body's own dharma, and the BG never asks us to starve them (indeed it forbids it, 6.16); Kṛṣṇa himself eats, sleeps and acts. The desires meant here are the saṅkalpa-desires: the imagined “if only I had this, I would be happy” that the mind spins endlessly. One may perform “bodily action alone” (3.8, 4.21) without incurring bondage. So the rule is not to kill the body's needs but to stop feeding the mind's fantasies.