After some time, the cutting mats for the Cricut Expression loses its stickiness. Here are my favourites for restoring adhesiveness so that the vinyl stays stuck to the cutting mat.
The UHU brand of glue stick works for vinyl. I apply it all over the cutting sheet and smooth it out with a putty knife. When it dries the adhesiveness can be reactivated with water. (UHU doesn't work for cutting paper though, the paper will undesireably stick to the mat.) I tried another brand of glue stick from the dollar store and it didn't work as well for vinyl tarps, so I prefer the UHU brand.
The other adhesive I like is Aleen's Tack-it Over & Over. This adhesive keeps a tacky surface for a long time. I don't know if is good for cutting paper with the Cricut Expression, since I don't use my machine to cut paper. (In fact, scrapbooking is one of the last crafts on earth I would ever be interested in. I did it for my kids using digital photographs and microsoft Word for when my babies were small, but after that, no way!)