If you use commercial metal cookie cutters (or make your own), it can be tempting to leave them to dry with your other washing up. That's a bad idea as it allows rust to get in at the seams and ruin the cutter. For best results, place your metal cookie cutters in your oven to remove any potential water left on the surface.
Luckily culinary weblog The Kitchn has a simple way of doing this -- after gently hand-washing the cutters, place them on a baking sheet and pop them in an oven already warm from baking. The few minutes it will take for the oven to cool should perfectly dry out your cookie cutters, help you avoid rust (and not use any excess energy).
Tip: Dry Metal Cookie Cutters in the Oven [The Kitchn]