Make sure you stand over your fabric while your cutting. Not having it the right height for you can effect how you cut. They have finger guards that you can get to put on your ruler. I've even seen some people put on safety gloves. If you make sure and keep your pinky finger on the mat as you hold your ruler straight that helps with slippage. It also helps if you get one with a squeeze handle that way the blade isn't out until you are ready to cut. The rotary cutter is a wonderful tool as long as you respect its personal space. =) Good Luck!

Is your cutting mat on a hard, solid service. One quilter was having problems because she was using her mat and rotary on the carpet. If I use my ironing board surface I do not get good cuts.

A level table helps too. If the table has slight dips in it that will make it skip too.

If its new, probably you are not putting consistent pressure, I have found this is often the problem with me. Just go slow, and always double check that all fingers are out the way. I am very careful to always lock my blade and be weary of where my hand is that is holding the ruler, and tap on wood have yet to cut myself in ten years. Also, the ergonomics of your table might be making it awkward for you to apply pressure, might be too high or too low

I got a batch of bad blades once. I thought I was going to pull my hair out because I thought it was me.

It may be also that you are too hesitant because it is so new to you. I watched my sister use her rotary cutter with such confidence whenI first started, and I was terrified. I often let her cut my fabric for me.

But it was lack of experience. Or at least I am now confident enough that I rarely have problems. Maybe you should practice on fabric that isn't something you care about?

Anyway, with experience....and a sharp blade...you will do fine.

Keep your cutter straight against your ruler and not on an angle. Use firm consistent pressure and stand so that you are over your work. I love cutting but I can't cut properly sitting down or if the table is too high. Get an experienced quilter to watch you and offer some suggestions as it may not be obvious to you exactly what is the problem. Also realize that cutting is not easy for a lot of quilters. When we have hands on at guild evenings, cutting is the least preferred job. It will get better with practice. Don't try to cut when you are tired or the light is poor. Stick on ruler guards are available if you are worried about cutting yourself. Also make sure to use Invisigrip or those little plastic grips on your rulers to avoid slips and slides. Good luck with this.

I used to use one of the white mats and eventually I had lots of skipping. I switched back to my olfa Green mat and all was fine.

what brand cutter?
does it happen to have two blades in it, rather than one?

This is so true. I had this happen to me and the fabric looked like I was shredding it. Those two blades together are almost impossible to see (smile). Great advice here. Check the blade!!