Put the translation stage and laser in proximity. Set up the relay mirrors so the laser beam will be sent straight along one axis of the translation stage. There are several types of translation stages, which will allow you to move the block of ice in the x-, y-, and perhaps even the z-axis; you can use a 1-, 2-, or 3-axis translation stage. The relay mirrors will allow you move the laser beam without moving the laser itself.
Place the block of ice on the translation stage. Fix the block to the platform so it doesn’t slide. You can do this with clamps or a rubber or cloth mat — anything that will keep the block relatively stationery.
Adjust the position of the translation stage so the laser hits at a corner of the ice block. Briefly fire the laser and then measure the depth of the cut. The carbon-dioxide laser will melt the ice, and this will give you an idea how rapidly the laser is melting the ice.
Move the translation stage and the relay mirrors, scanning the laser over the surface of the block. Fire the laser for the amount of time necessary to reach the depth you need. You can poke the awl along the carved hole to check how deep the laser has cut.
Continue scanning the translation stage and adjusting the mirrors until the laser has been scanned over the entire surface.