You need to visit your local Woodcrafter’s. If there isn’t a Woodcrafters in your area, call the local university student union and ask if they have a shop you can use. If you can find a BAND SAW, that is the tool you need. You will need a fine blade, not over 1/4″ and you must test your material at different speeds. A band saw is the correct tool because the blade goes in the same direction, with the teeth pointing and pulling down. If a blade pulls and pushes up, it could easily tear the paper you glued to the plywood.
Good luck.

suggest starting with exacto utility knife to cut around shape of paper image, then carefully cut the wood with same tool about 1/8 , then cut from back side if able.

Also a thin fine bladed jigsaw tool if possibly,

~also suggest leaving original and copying/scanning picture, or buying another, then cut paper and wood separately then glue or laminate together after,
. .

Hi you need a Dremel cutting Kit.
“Dremel 400 Series XPR Rotary Tool Kit w/ 90 Accessories
Model 400-6/90″

The wood is thin and you want a precise cut because your basically carving.

Now if you want to cut something out, the Dremel will work just as well for a piece of wood that thin.

If you go thicker on the wood and your trying to make a cut out, not a carving into it, then you will want to get a
*Scroll saw *.

Make sure you sand everything so that it will have a smooth finish.

Depends on how much detail in your cuts. A more elaborate and ornate cut will require a thinner blade, such as a coping saw. (like a stubby hacksaw with blade that is very thin and narrow. If it is with fairly large curves and no sharp points, you can get away with using a scroll saw or a hand held jig saw, but you will have to use a very fine toothed blade, which will make it pretty slow going. (don’t force the saw blade!)

Next time, try mounding the poster on foam core, instead of wood. Cuts much easier with hand tools and, as long as your cutting stroke goes BACK, to the mounting board, the poster should remain unfrayed.