Desire becomes blind and starts destroying the mind.
Literal
Desire [topic-は] blind [into-に] become-and, mind [object-を] destroy-begin.
盲目になる ('become blind') is a metaphorical use of 盲目 ('blindness'). 始める ('to begin') attaches to a verb masu-stem (破壊し) to form 'begin to X.' A literary/aphoristic sentence about human nature.