Yes. Set the wishlist to Invite only and the link you already sent stops working — anyone who opens it will see a "No Access" page. If you'd rather remove the wishlist entirely, you can delete it. There's no separate button that turns off just the link.
Steps
To stop a shared link from working:
Open the wishlist.
Go to the Share tab in your wishlist settings, in the section that controls who has access.
Change the visibility to Invite only.
Once it's private, the old link no longer opens the wishlist. Only you and people you specifically invite by email can see it.
Good to know
The share link is tied to the wishlist itself, not a one-time code, so there's no "regenerate the link" or "deactivate the link" option. Changing visibility to Invite only is how you cut off the people you sent it to. And if you later set the wishlist back to Anyone with the link, it reuses the same link as before — so the original recipients can open it again.
After you make it private, decide who should still get in: invite those people by email under your wishlist's access settings. A plain link won't work for a private wishlist. See "How do wishlist privacy settings work?"
Deleting the wishlist removes it for everyone. Any reservations on it are cancelled at the same time. This can't be undone.
Making a wishlist private doesn't change who can edit it. Editing access is a separate email invite and isn't affected by visibility. See "What's the difference between an editor, a guest, and someone reserving a gift?"