By Contemporary Standard American English standards comma placements are strewn throughout the sentence with very little regard for clarity (removing a few would make it clearer), and the logical relation between clauses leaves something to be desired.
Standards for comma usage weren't established until almost the end of the 19th century. Some people used breathing or personal stylistics to decide on comma use, but there certainly was no general expectation that it would follow grammatical construction or logic.
Compared to some other 18th century documents I've read, the US Constitution is downright spare with commas.
However, by the standards of English then in effect, it makes perfect sense. Part of the problem is that written English prior to the 1900s included a large element of (conscious or subconscious) verbalization of what was written.
Try reading the Constitution out loud, taking appropriate breaks at the punctuation. It becomes a lot easier to understand and read; most (but not all) of the ambiguity will disappear.
