I had a similar problem once; the blade went thump, thump, thump; carried it to a quilt shop for help. They took it apart and compared with an identical one, and there was a part missing. So I had to buy a new one. BlueBars

aixia, do you mean slivers in the fabric, or the mat itself? I have two rotary cutters and with the one I assumed would work best with this mat, I often had trouble getting the blade in right at the beginning of the slot, and it would cut into the mat, making a jagged edge which caused more snagging next time I tried to cut -- the situation was getting worse and worse. SO I tried my other rotary cutter which is a self closing one. I thought it would be even HARDER to get in the slot 'cause the blad is against it's plastic guard until you press down-- but it worked FLAWLESSLY with it! Slides in simple and perfect every time and never snags!!!! The one that DOES work GREAT with it looks like the one at the link below. I was surprised 'cause I don't like it as much with my regular ruler. Here is a link that might be useful: Pressure sensitive rotary cutter

They do work if the blade is just a bit dull, but not if it's very dull. They will not polish out any nicks in the blade. That said, the blade is never as sharp as a fresh blade, it's a royal PITA to use, and I found the design a bit dangerous. The blades often slipped around, creating a risk of slicing off a finger or two. There is a lot of "handling" of the blade during the process (out of the cutter, into and out of the sharpener a minimum of 4 times, back into the cutter) and every step with the risk of cutting yourself. I tossed mine, and consider the money wasted.

You can---I have read of a company that you send used blades...they return sharp ones for a fee less than buying new. Do a Google search. The company escapes my memory at this moment.