There's a good chance you'll get this just trying to finish the game. However if you want to grind out rope cuts (or find yourself needing them after completing the game/other achievements), Level 1-7 has 6 that can be cut in one circular finger swipe.
When you cut the ropes the candy will fall off the screen (counting toward the losing candy achievement) and restart the level automatically. You do not need to "finish" the level, wins and losses both count. Eskobar also confirms in the comments that if you are done with your candy losses, you can cut and hit restart for even faster progress.