“Desire is death” means that the speaker wants his lover so badly that he feels like he is dying.
In “Sonnet 147,” the speaker is infatuated. This means he feels a very strong, unmanageable love for his beloved. He can think of nothing else but wanting her. This wanting is the same as death, because it is so painful. He can think of nothing else.
Desire is death, which physic did except.
This means that there is no cure. There is nothing the speaker can do to get out from under the obsession. He describes himself as past “cure” and “past care” because he is completely under her spell.
This pretty sonnet explores the darker side of love, when it turns to obsession. There are less than positive effects from love sometimes. Something that starts out wonderful can turn sour.