Nothing you upload ever leaves your browser
Crop Your Design has no server that accepts images. There's nowhere for a photo to go even if something wanted to send one. That's not a policy we ask you to trust; it's something you can check yourself in under a minute.
(The only network activity you'll ever see is the one-time page load itself: the app arriving to you. That's different from your photo leaving.)
When you pick a file, your browser opens and shows it to you the same way it would preview a photo before you attach it to an email, entirely on your own machine. What you see in the crop tool never travels anywhere else to get there. Closing the tab clears it completely; there's no copy sitting on a server afterwards, because one was never made.
Want the technical, browser-vendor-authored version of why this is possible? MDN's File API docs explain the underlying web standard.