ロープを切るナイフがほしい。

rope

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to cut; to cut through; to perform (surgery); to sever (connections, ties); to turn off (i.e. the light); to terminate (i.e. a conversation); to hang up (the phone); to disconnect; to punch (a ticket); to tear off (a stub); to open (something sealed); to start; to set (a limit); to do (something) in less or within a certain time; to issue (stamps, vouchers, etc.); to reduce; to decrease; to discount; to shake off (water, etc.); to let drip-dry; to let drain; to cross; to traverse; to criticize sharply; to act decisively; to do (something noticeable); to go first; to make (certain facial expressions, in kabuki); to turn (a vehicle); to curl (a ball); to bend; to cut; to shuffle (cards); to dismiss; to sack; to let go; to expulse; to excommunicate; to dig (a groove); to cut (a stencil, on a mimeograph); to trump; (in Go) to isolate (an opponent's stone); to start a fire (with wood-wood friction or by striking a metal against stone); to draw (a shape) in the air (with a sword, etc.); to finish; to complete

knife

indicates sentence subject (occasionally object); indicates possessive (esp. in literary expressions); but; however; still; and

wanted; wished for; in need of; desired; I want (you) to