adhesive on cutting mats.
I wash my cutting mats at the kitchen sink. Water plus a few drops of any kind of hand dish washing soap. Then let the mat dry. You can do some blotting off of the water with a paper towel but once you feel even a slight sticking stop blotting and let it air dry for the finish. Of course it does not matter on the backside where there is no adhesive, just finish drying it with a paper towel if you wish to do so. Buying wipes adds expense that is not needed unless you don't have a sink or bathtub around.
The water releases some of the paper fibers that pulled off the paper and stick to the mat. Those fibers are what creates the loss of adhesion so mostly its a matter of getting the fibers off. However some of the fibers will never come out of the adhesive and some of the adhesive will transfer to the back of your paper so eventually you will need to apply more adhesive. This is easy to do, just mask off the edges of the mat that typically don't have adhesive on them and apply a coat or two of light duty repositionable spray adhesive.
Another method of renewing the adhesive is to apply a coat of Aleene's Stick it Over and Over that has been thinned 50/50 with water. Here is a video on that.
https://www.youtube.com/watch?v=_QUfPpiw1kU