I have a Big Board (they are fantastic! and no I don't have any connection with them!) which I place next to a wall.
To cut strips:
First , I put my fabric on the board with the center folded to the selvedges taking care to make sure all is parallel to avoid the dreaded V-cut.
Next, I square up my 24" ruler narrow end against the wall.
Then, I move the Big Board mat until the fabric is absolutely parallel to the wall using the ruler pushed against the wall. I move the ruler sideways to make sure all the fabric is parallel.
Finally, as I cut I hold the ruler down with my hand and keeping the ruler in contact with the wall.
Works great until I forget how to measure and cut a strip 1/2" to narrow!! What's that about measure twice and cut once!
Even small pieces can be cut the same way, by adjusting the mat to keep the ruler perpendicular to the wall. I DO NOT use the marks on the mat as my guide, only the ruler. AND I do use TWO rulers placed side by sid: one for measuring and the other for cutting against, just moving the measuring ruler to the side after setting my hand on the other ruler when ready to cut.
Let me know how it works for you.