Then this isn't the project for you - you'll need much more experience to get something like that going from scratch. For starters, that's entirely the wrong laser diode you have for an engraver. You either need a CO2 laser, Nd:YAG (or other DPSS laser) or a large fibre coupled laser. Something that emits a single, round, tight beam. These diodes emit 19 "stacked" beams that are more like flashlights than laser beams. Very difficult to correct them into a proper usable beam, especially for a hobbyist.
Start with a small laser engraver kit perhaps and go from there.
Yes, IR diode bars aren't good for much more than optical pumping.
500 what? 500 USD would be plenty to buy a complete CO2 laser cutter. Just the laser actually costs more than a complete system somehow, according to ebay prices, so this is not a cost-effective project from the start.
I hope it's not your national currency, because google tells me 500 Ukrainian Hryvnia equals 20.143 US Dollar, which will buy you nothing.