Yes, it is important to clean off rubber stamps after use, particuarly when switching between colors.
Wood-Mounted Rubber Stamps
Do not use soap and water with wood-mounted rubber stamps, because it will loosen the adhesive and compress the cushion foam. The quickest and easiest way to clean your wood stamps is with a damp (not wet) towel.
Some inks can stain your stamps, StazOn ink, for example. It won’t ruin your stamp just stain it, and you can just clean off what you can and let the stamp dry. To get them really clean, you can use the StazOn cleaner.
The quickest and easiest way to clean your acrylic stamps is with warm water and a mild soap. For really stubborn ink, you can also take a soft, old toothbrush and gently scrub the crevices in the image.
Please don’t use acetone, bleach or any oil-based cleaner for either acrylic or wood-mounted stamps.