I cut my great big mat that fits on a big cutting table with spring loaded scissors, no problem.

I used my Henkle scissors, worked like a charm!

I cut one of my older ones into smaller ones, after cutting it, there was 1 part where the numbers were off, I used a marker and just re-numbered...they are great when I am toting to my quilt guilds...I used a pair of older shears, and it didn't seem to hurt them...but I made sure the pair I used were old, I only use them for things that if they get messed up it is no great loss...

My DH measured mine and then went to the shop and cut it.
I belive he used his table saw, but I could be wrong. But I have a very nice straight edge. We topped one cabinet with that cutting mat. Since there was mat left over, he made a mat the size of my machine bag, so I always have a good quality mat with me when I travel.

Perhaps a linoleum knife?

You would cut the Martelli mat? Well, the demo at the quilt show showed us the Martelli rotary cutter will cut metal Coke cans, cardboard and then fabric. It should cut a mat, I would think.
Missed you at the Plano Quilt Show.
Are you going to Debby's retreat?

My DH used a saw out in his shop -- not sure which one. Then he gave it a fine sanding. He cut one smaller for me, put it on a board and mounted the board on a lazy susan thing -- I have my own turn-table mat!!!

use a utility knife and a ruler to score the mat several times then it will be easy to cut with scissors. You can score it until it cuts through but be sure the underneath surface is protected or not cared about.

Box cutter worked for me.

Exactly what I do!