I use the June Tailor Shape cutter all the time. I have added little dots of "sandpaper" on mine to help prevent slipping. I use an Ergonomic cutter, the Martelli cutter ( I have bad shoulders/ 3 surgeries) also, it helps to keep one finger, such as your pinkie off of the ruler and on the mat to help stabilize it. As I cut further down the mat, I place my hand near the line I am cutting. Keep your cutter up right, don't lean to left or right, that caused you to move the mat ant your cutting line.
Try an ergonomic cutter, that might be easier for you to use
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My newest Grandson, Caleb Austin, was born May 29th. I am now Grandma to 4 precious babies. I am so blessed!!!!