Spray adhesive.

I have a client who is interested in using Elmer’s Board Mate spray adhesive to attach paper to thin birch plywood to be laser cut. I’m concerned as to the safety and outcome, anyone have any experience here.

I would think the biggest issue would be the paper igniting. The spray adhesive is thin and if allowed to properly dry shouldn't have enough solvents to add much to the flammability.

You can buy a laser-safe rubber mat that paper kind-of sticks to while being cut.
It's not cheap, but if you have 50+ wedding invitations to laser, it's worth having it!
Or use some small weights.

I'm assuming the birch is just acting to absorb the beam beyond the paper? If so, won't the wood stain the paper? And if that's not an issue, why not just cut onto the back side of some lasersteel and use magnets to hold the paper? The lasersteel will still be usable after you're done-

-or- I've never tried this (I don't do much cutting) but I'm thinking a 1/16" thick sheet of Teflon or silicone mat would be good to cut into- Teflon is very heat resistant, so is silicone, but it WILL engrave- however once a few passes have been made the silicone would pretty much ignore the beam, whereas wood would likely keep smoking.

Thanks for the input friends, I should clarify that what we would like to achieve is to glue the paper on the birch ply and cut through both, I have a good deal of experience with cutting paper and ply just not together. I have good exhaust, as long as no nasty fumes hurt my laser, I should be good, I hadn’t thought about the effect the wood burn will have on the paper so I’ll let you know. This client has been fun and we have had good success with his other projects, since he gave me the green light (and the green) to try a sample I will try to post some pics.

You're not going to hurt your laser-- :)

I'm thinking your worst enemy in doing this would be 'normal' air assist and exhaust flow. Good example is engraving red Rowmark. My Gravograph's exhaust pulls LOTS of air across the table, great for removing smoke but the smoke travels across the work, leaving soot behind. And if using too much air assist, same thing pretty much. What works for me is to reduce both the exhaust flow and air assist. I should point out that I DON'T use air assist for cutting, but ONLY for lightly pushing smoke out of the way and to prevent flareups. With the right amount of air, pointed AWAY from the cut somewhat, does what I need. And reducing the exhaust flow so the smoke can drift around a bit keeps the soot to a minimum...