The short answer is "you can't".
The long answer is "maybe someday you'll be able to do this, and you can help a little bit in getting to that day", but we'll get back to that later.
I don't use reddit, but from a quick look at their Markdown guide (okay, technically, that link isn't official, but their actual official page links directly to it), it looks like a superset of Stack-flavored Markdown.
The easiest workaround in practice is to not use the following things in reddit, or manually remove them when copying to Stack:
^
for superscripts
~~
for strikethroughs
>!secrets!<
for spoiler blocks
- any kind of table formatting (alternatively, do use it, and wrap it all in a code block when it's on Stack, even though that's semantically wrong)
The reason for all of this is that Markdown itself started out as an imperfect spec, according to Jeff Atwood, one of the co-founders of Stack. As a result, different places made up their own variants with the gaps filled in in ways that were helpful for their individual use cases.
To try to deal with this, Atwood and a few others, including people from both Stack and reddit, started an initiative called CommonMark—although it wasn't always called that; there was some unpleasantness with the guy who created Markdown, the venerable John Gruber of Daring Fireball—which is where you can help (see, I didn't forget what I said at the top of this answer).
CommonMark has a "How can I help?" page that (over)simplifies to "write some code" and "use the thing". On top of that, you can try to lobby various places on the Internet to switch their implementations to CommonMark. For CommonMark here on SE, see Will CommonMark be adopted for SE?.