The other day I found these two sections of a tree trunk in the street. So I'm wondering, can they be prepared to be used as some type of rustic stump table?
This question is a little broad, but I'd say yes, you could make a table out of these.
I'm assuming you're going for a "found object" style, and you're not talking about using them as lumber to make a "normal" table.
You'll run into two main challenges here, flattening the endgrain and checking.
The first problem is, how do you get them to sit flat and how do you get the top to be parallel (i.e. level)? For this I'd probably recommend either a belt sander or a low-angle plane. Flattening the bottom is as simple as removing the high spots until there are none. To make the top parallel to the bottom measure up the side a set distance from the bottom at several points around the piece and remove material until you hit all of these marks.
The second, and probably more important, problem is checking. As the wood dries it shrinks more radially than it does axially. This means that it will attempt to tear itself apart, with cracks forming from the center outward. As it is it will take several years to dry, and it will continue checking the whole time.
There are several ways you could try to deal with this, but I think the easiest would be to just embrace the natural process. Let it dry for a few years and develop checks, then fill in the voids with resin or epoxy.