There's a reason why - outside of the various experiments by hobbyists and others - you don't see any low-cost semiconductor-based laser cutters or engravers.
The main reason is cost per watt.
If you start to price out what it would cost using semiconductor lasers (either monolithic or combined beam) to get the same wattage as a gas tube laser, you quickly find that gas tube lasers are much cheaper per watt - at least currently.
Furthermore, there's a question of what wavelength to use - which will effect your choice of what laser to use. As noted by Sam's Laser FAQ on Carbon Dioxide Lasers:
"Unlike the other lasers producing visible or short near-IR light, the output of a CO2 laser is medium-IR radiation at 10.6 um. At this wavelength, normal glass and plastics are opaque, and water completely absorbs the energy in the beam. The 10.6 um energy is ideal for cutting, engraving, welding, heat treating, and other industrial processing of many types of materials including (as appropriate): metals, ceramics, plastics, wood, paper, cardboard, fabric, composites, and much much more."
This is why you see such cutters and engravers use a CO2 laser tube - it's the proper tool for the job in the majority of cases.
In fact - I would highly encourage you to read the entirety of the Sam's Laser FAQ as it will likely answer all of your questions on lasers, usage, and safety.
Basically - you are likely to spend more money on trying to create a semiconductor-based laser cutter or engraver - and the results will likely be disappointing - than if you spent the money on a proper laser cutter/engraving machine.
Something you need to ask yourself is "what is my goal?" - is your goal to experiment and learn about how to build a laser cutter (even if it doesn't work or works poorly)? Or is your goal to be able to actually process materials for a project using a laser cutter?
If the former, then continue to play - just be aware that you may spend a lot of money, time, and effort - but if this is worth it for the learning experience to you, then go for it. If, however, your goal is the latter - then trying to build your own laser cutter is not likely the best choice; you would be better off spending the money on a pre-built device. There are many options available, for fairly low costs (depending on how much you plan to use them - none are really low cost if you don't plan on using them fairly often).
There's always the small and low-cost (under ~$500 USD now) Chinese laser cutter/engravers; just note that while these are low cost, then can be very finicky to get working from what I understand; here in the States, we have a company in Las Vegas (Full Spectrum Laser) that imports them, does the "re-work", then resells them at a higher price (basically making sure things work properly for the end buyer).
The next step up - while still giving a DIY option (to an extent) - is this kit - which honestly I think is the best "bang for the buck" - if you are willing to spend the time putting such a kit together.
Beyond this, you are looking at machines by companies like Universal Laser Systems - the "name brands" in laser cutting/engraving - and they have prices to match. But they do have top-quality equipment.
Something to note when it comes to laser cutters that use CO2 lasers (mainly the water-cooled tubes; the ULS systems acutally use (I believe) an RF excited tube that is air-cooled - which is a different tech) - is that the more you use the tube, the longer it's lifespan - so if you decide to go down the route of building your own laser cutter using a tube, purchase the tube last; also if you purchase a pre-made machine, use it often to get the maximum life out of the tube. In other words, tubes for CO2 lasers have a shelf-life, and they pre-maturely fail the less they are used.
Also - if your goal is materials processing - then you might also look into a CNC router; while not as fast as a laser cutter, it can typically do the same kind of work, provided you don't mind the wider kerf - that is, the width of the cut (I think of a laser cutter as a CNC router with a very small kerf).
Finally - note that whether you use a laser cutter or a CNC router - you are going to have to deal with a "mess" - in the case of a CNC router, it's a bunch of "dust" that you'll have to vacuum up and keep clean. In the case of a laser cutter - you have to deal with smoke and gasses created by the "cutting" process. You need to have some way to ventilate the machine, possibly scrubbing the gases (mainly for smell), and also deal with not letting the gasses/smoke get on the lens/mirrors of the machine (so you usually need a compressed air-source as well directing a jet of air at the exit aperture). Also with a laser cutter or engraver - never walk away from the machine while it is in operation (this especially includes homebrew builds). The material being cut or engraved can catch fire - so you need to be able to watch for that and take measures if needed, to put it out. Also - never cut PVC in a laser cutter - it'll release chlorine gas (poisonous). Never cut styrene (or foam board) - it'll easily catch fire.
I'm going to stop here - I've almost written a book. I don't have a lot of experience with laser cutters (I've only used one - a ULS 60 watt job at my local TechShop), but I have studied the heck out of things (up to and including homebrew CO2 lasers - which you want to stay away from if your goal is to make a cutting machine); ultimately, if I do get a machine of my own, it will either be one from that company in Vegas, or that kit I mentioned. But then again, my goal has been to have a machine to cut things - not to learn how to build them. Your goal(s) may be different, but you need to consider them first.