Glass Cutting
It's not uncommon for thicker glass be annealed, not tempered, for a table top. This is due to the amount of force required to break it.
From what I've been told growing up around a glass shop and working in the industry for a number of years, the reason glass cutters work is that glass, stone, etc will always break at the greatest point of stress.
When you apply pressure to the surface of the glass with a glass cutter you are crushing the surface under the wheel which causes heat. Oiling the wheel on your glass cutter will help maintain this heat evenly for a longer period of time. You need to break the glass along your score before it cools in order to get the most reliable break.
Thick glass, 1/2" and greater is very difficult to cut even for the very experienced. It also takes a much greater force to break after scored. If this is your first attempt at cutting glass I would recommend getting a few scrap pieces of thinner material and practicing on those to get the feel for scoring and breaking the glass. The thicker the glass the harder it becomes to cut off a small amount. Even 3/8" can commonly break roughly and required a belt sander to polish the edge smooth. Breaking 3" from a 1/2" thick piece of glass will be difficult and I would personally opt for a wet saw.
Also, any time you cut glass the edges will become sharp. Be sure to use sandpaper to smooth the edges, called a seam, in order to help prevent cuts.
Glass Cutters
As far as cutter brands, I prefer Silberschnitt because the brass has a nice weight to it and I've grown accustomed to it. Fletcher is probably the most common brand I've seen from shop to shop. Someone that cuts glass daily is more likely to go with a cutter that is self oiling and is filled in the end.
The cheaper "hobby" cutters do the job just as well. The most important thing is the wheel. A carbide wheel will last you longer, but for limited usage a steel wheel will suffice. If you opt for one of these types of cutters be sure to rub 3-in-1 oil on the wheel prior to scoring the glass.
A hone angle of 140° is the most common. After enough experience 140° is easy enough to turn when needed, but broad enough to be effective for 1/4" or 3/8". I've used it for glass with a thickness up to 3/8". A hone angle of 154° is what is used more commonly for greater thicknesses. This angle will give a broader score allowing for more surface stress distributed along the same line allowing for a more reliable break. A 120° angle is more often used in artwork and difficult pattern cuts. A more acute angle is easier to work with and what you want majority of the time. The greater angle is more difficult to work with but necessary to control a break on thicker glass.
First off, have you considered how heavy this tank is going to be when full of water? The total weight of the water contained in a 31.5"x25.6"x25.6" tank is 744 lbs.
The total force on each wall is a function of pressure, depth, and wall area. Integrating all of that over the surface gives a total outward force of 459 lbs on each side.
You'll need to know the ultimate tensile strength of the particular type of glass you're using. I'd recommend looking for tempered glass, which will have a higher strength.
For a rectangular plate of toughened glass supported along all edges (meaning, including a top brace), I found the following generalized formula for a maximum uniform pressure loading (PDF link):
Pmax (psi) = 84000*t^2/Af
where t is the glass thickness in inches
A is the area in square inches
f is the safety factor (10 in this case)
(I'm pretty sure it's supposed to be the thickness parameter that's squared, not the constant as it was written in the source material. Also take this number with a grain of salt, since the source material has an apparent typo in the equation. Wikipedia has a much more in depth derivation here.)
Using the parameters you specified along with a safety factor of 10, the max allowable uniform pressure loading is 2.2457 PSI. So your choice of materials should be OK for the non-uniform loading with a max value of 1.138 PSI. Note that this is for a piece of glass that is fixed along all edges, so that would mean you've got it secured to a brace along EVERY jointed vertex to counter the bending moments at the edges of the plates.
Also consider the strength of your adhesive if you're set on going frameless. It's going to be under a max stress of about 8.04 lbs/linear inch, in both shear and normal stress if you're doing the corners as butt joints.
Best Answer
Standard EMT tool for tempered glass car windows (after taping - packing tape preferred over duct tape) is an automatic center punch. A hammer and nail will work the same, it's mostly being a one-handed tool that's easy to carry that makes the ACP the preferred tool among EMTs.
If you're "smashing the whatever" out of it, you're doing it wrong. It just takes subtle application of force to a fine point. If you get lots of long shards, it wasn't tempered, and you'd need to be careful handling the shards (movie reference and graphic explanation of the desirability of tempered glass - the non-tempered glass in "Christine")