marcros,
If the 6mm acrylic you've got to cut is not too long, and as the cuts are only straight lines, personally I wouldn't bother with a saw at all.
You need a "scrawker" - basically an old bradawl, screwdriver, etc, with a small sharp hook/notch ground on the business end.
Support the sheet on thick rags, an old towel, etc, mark the cut position at each end of the sheet with a fine marker pen, line up a steel straight edge on the marks, then "scrawk" along the length - as it's 6 mm, you'll probably need fairly good hand pressure and about 4 scrawks in all, but it's not necessary to go all the way through the sheet.
Then turn it over, support the uncut side of the sheet with the steel straight edge flat on the bench with the straight edge close under the scrawked mark and press firmly downwards (like they do to cut sheets of glass in the glass shop).
It will break off quite cleanly, though at 6 mm, being quite thick, it may need a quick tidy up with some abrasive paper afterwards.
Your "scrawker" tool needs to have a pretty fine hook/point ground onto it, otherwise you'll need to make an allowance for the thickness of the tool when setting out your final measurement, because, as said above, 6 mm is quite thick for this trick. But I have often done this, including thicker sheets of acrylic once in a while.
You can also use a smoothing plane or block plane to trim to final size if necessary - the main point being that both the scrawking and the sanding/planing are done at hand tool speeds and don't therefore promote the tendency for the 2 cut edges to melt together again during cutting and trimming.
Acrylic is pretty soft stuff really (in comparison to any wood except perhaps balsa) and provided it is well supported during the operations, won't give you any problems at all with cracking, etc.
But as I'm sure you already know it scratches pretty easily, so if the finished item is for show, make sure you keep the backing sheets in place until the very last minute.
HTH
AES