Another answer has already given the basics:
- Piercing is only part of cutting
- The blade behind the edge is still subject to friction
There are a few additional points specific to blades made of real-life materials, however, that may be of value in thinking out what your superlative weapon can and cannot do.
Terminology
To do this clearly, we need some basic terminology.
Edge: The edge is formed where the two bevels meet.
Bevel: The bevels are the flat parts that extend directly back from the edge at an angle.
Centerline: If you a draw a line from the edge to the spine, this forms a single line. The angle of a bevel is measured from the centerline with the vertex at the edge.
Flat: The portion of a blade that runs more or less parallel to the centerline, often incorrectly called a bevel (or, in reverse, bevels are mislabeled as flats).
Friction is an issue along the edge while dragging, and along the bevels and flats when deep into a cut.
Teeth
All blades have teeth, like saws. These can be large or small, evenly or irregularly spaced, consistently or inconsistently sized. They can be perfectly in a line, splayed, or in multiple parallel lines.
When you try to cut something, you normally slide somewhat along the teeth. This is much the most efficient method. Each tooth penetrates in sequence, splitting the gap further open as you go along.
Because obsidian is volcanic glass, the teeth may or may not be parallel or in a line. Because the material has to be napped, the teeth will tend to be irregular in size, shape, and spacing.
This means that if the blade was originally just traditionally-napped obsidian your cuts will always be jagged. No matter what you do, your blade is always going to act like a serrated bread-knife or steak-knife.
Shape (Profile)
With a real knife, if you had ultra-tough-and-hard materials, you'd polish the edge to bring all your teeth to a highly regular pattern of consistent size, but this blade can't be sharpened. And that's a problem.
If you have materials that just won't break, the obvious thing is to grind the bevels to as narrow a total included angle (the angle of both bevels added together) as you can manage, then refine and polish the teeth until they're super-small and perfectly even. This is how a razor is made, for instance. Normally, you don't do this with a weapon, because as soon as you hit something it'll crush, but that's not a problem here.
This pattern is ideal, because your knife won't wedge. That is, it has very narrow shoulders, because the bevels are extremely thin. When you cut, the friction of the cut material against the bevels is a significant part of what stops you from sliding through easily.
Unfortunately, you can't sharpen this thing. Since it's impossible to break, it's impossible to abrade. So you're stuck with whatever profile you started with.
Cutting
Once you focus on the fact that your blade is always a saw, you'll realize that the usual smash-with-the-edge approach we associate with swords is grossly inefficient. The best thing is to drag the edge as you hit. So how well will your obsidian weapon cut?
The more regularly-spaced, narrow-beveled, and small the teeth--and the more they are all precisely in line along the centerline--the better it will cut.
If nothing can crack those teeth despite a gross lack of supporting material (very narrow bevels), then the thickness of the blade at the spine can be ridiculously thin. This will dramatically reduce friction. It will also make your blade weigh far less. Normally weight in swords is a serious problem, since steel is very heavy, but a very thin blade won't have this problem.
Conclusions
You need first to decide what this thing looks like. Does it look like a thin, elegant sort of straight katana, but black as night? Or is it a massive, primitive chunk of death, with big irregular fangs? That will tell you what the tooth pattern should be.
Next, decide how heavy it is. Obsidian's volumetric mass is about 1/3 that of steel, for comparison. Bear in mind, if you make comparisons to extant swords, that many swords are not solid steel precisely because it's so darn heavy (katana are the most obvious example here). From a rough weight--say, that of a baseball bat?--you can work out the volume of the blade.
Once you know that, you can decide how thick you want the blade to be at the flat, and how wide you want it from edge to spine (or if it's two-edged, from edge to edge across the spine).
With all that in hand, you can work out quite easily how the thing is most efficiently used. Probably the best is going to be to hit somewhere around the lower third of the blade and then, while continuing to press as hard as possible, to drag the haft backwards. If the teeth are small and regular, it'll glide through anything; if they're large and irregular, it'll go clunk-clunk-clunk and make a nasty gash. If the bevels are narrow and the spine thin, it'll soon be a very, very deep cut; if wide and thick, not so much.
