I intended to reblog this with commentary, but I failed, so here goes: If I remember right (back in the 1980s), it's an "Other Than Honorable," not DIShonorable discharge. You have to do something a lot more heinous to get a dishonorable.
Also, I knew guys who got caught with weed or hash on them, or got caught in a piss test, or a couple who got caught buying, and all they got was a reduction in rank, confinement to post, and some extra duty. You had to make a HABIT of it to get kicked out. Like, fail multiple urinalyses or something. So the one joint thing won't work unless they've REALLY cracked down, and even then, you'd have to actually get caught red-handed, or have smoked close enough to random UA.
There's also a discharge for something like, "unable to adjust to military life," which if I recall correctly was a General Discharge. Basically, if you're just enough of a fuck-up, they'll try to force you to fit the mold for a while, but if you keep it up, they'll boot you out.
Now, these are all assuming you're already in the military, but if you're NOT, I have good news: There are several kinds of folks who, in the past, at least, were exempted from the draft.
These include: Ministers and divinity students, Sole surviving sons (if a family member died in U.S. military service or is MIA), Elected officials while in office, Veterans (in peacetime), Conscientious objectors (with proven moral or religious beliefs), Students (temporary postponement until graduation or semester end), Individuals with qualifying medical conditions (classified 4-F), and Those facing severe family hardship.
Now, I can't guarantee they will honor any of those exceptions if a draft is reinstated, because they can change the rules on a whim. Example: For a time in the 1960s they wouldn't take those who had gotten married before a certain cutoff date, and later amended that so they wouldn't take married men with children, but they dropped both of those exemptions.
A lot of people avoided the last draft by leaving the country, but unless you have a valid passport that can be difficult, and even if you do have one, you're likely looking at becoming an undocumented immigrant in that country. (Canada was sympathetic to US folks crossing the border to avoid service in Vietnam.)
One simple thing you can do to maximize your chances, though is:
Register as a Conscientious Objector.
Now, this could backfire, of course--considering under the current regime you can be charged as a terrorist for attending a protest in which someone else gets violent, or for possessing the "wrong" kind of literature, so I cannot guarantee the government won't simply declare all conscientious objectors to be terrorists.