if you are afraid of cutting yourself get the "clutz glove" - it even has little grippies to help you hold your mat.
Also, make sure your hip is aligned with your shoulder and directly in line with where you are making your cut. if you don't then you could be leaning the blade left or right which will result in poor cuts.
Definately worth going to a LQS and asking for help. Or ask a friend for a cutting demonstration and then ask to have your technique watched to see if you need any adjustments.
Good Luck!