I cut some cheapo table mats (£ store-type things). Also some wine bottle corks (real ones, unused), both for my wife.
The table mats were a bit crumbly (the compressed bits of cork in the mats looked a bit large and coarse), but in the end, by cutting a bit away from the line and light sanding afterwards, the result was OK. They were about 5 or 6 mm thick BTW, and she wasn't after high precision cuts, "near enough was good enough". I used no sacrificial backing.
Cutting the corks was fine and produced good smooth cuts, no trouble. I cut them in half (along the long axis) and in half along the length.
It would probably have been just as easy to cut both with a really sharp knife, though I didn't try that (my wife bought my Excali for my birthday and I wanted to use it at every opportunity).
In both cases I used a pretty fine blade (about a 2 or 3 if I remember correctly) and slow speed/light feed pressure. My wife was pleased.
AES