How should I cut these speaker stands down to size?
The bases of the stand look as if the pole is welded to it. Unless you have welding skills, cutting at the base probably will not work.

The top appears to consist of a thinner pole that the speaker is attached to, inserted into a slightly larger pole that is attached to the base. In addition, there is a locking knob that seems to go through a threaded hole in the outer pipe, which probably presses on the inner pipe, allowing the speakers to be raised higher.

You probably need to cut down the outer pipe the same amount that you want the speakers to drop. This will eliminate the adjustable mechanism, but you may not care. If you need adjustable, you could drill and tap (thread) the outer pipe lower down, but that is a hard job needing specialized tools. You could solve it by drilling a series of small holes in the inner pipe and using a small rod (even a large nail) put through one of the holes and resting on the top of the outer pipe.

Depending on how long the inner pipe is, it may not allow the speaker to drop to the newely lowered outer pipe level.  In that case, you need to cut a section off the bottom of the inner pipe.

Several other answers address how to cut the pipe. Many of them will work, depending on the tools you have.

Once you insert the inner pipe into the shortened outer pipe, you may have some rattling since you have eliminated the locking knob.  This can be cured by wedging a small sliver of plastic between the inner and outer pipes (sometimes even cardboard will do). You also could create an alternative locking system by working out a clamp at the top of the outer pipe, but if you are not adjusting, that may be too much trouble and would not look as neat.

SUPPLEMENT: Based on the additional picture, you have a plastic grommet that tops the outside pipe. Once this is inserted in the cut down pipe, it will probably eliminate any rattling. If it does not, you still can wedge a small wire or plastic piece between the inner pipe and the grommet to tighten it up.