How can I turn off a coupon without deleting it?

Go to Marketing → Coupons and click Disable on the coupon's row. Its Status changes to Disabled and shoppers who try the code see "Invalid or inactive coupon code".

When you want it back, click Enable on the same row. All its settings and its usage count are kept.

You can also untick Active inside Edit and click Save coupon. Use Delete only when you never want the code again.