There's no legal mechanism in the US by which TikTok could be outright banned. Apple and Google could drop it from their app stores if pressured enough, but even that wouldn't be a government action.
They could require ISPs to block access to the servers, as they've done (poorly) for a range of websites.
They could classify TikTok as entertainment, and then it give it the dreaded "Refused Classification", making it illegal to distribute or make use of.
They could ban it under the Australian Customs Act, forcing places like Google Play to remove it from their stores, as they've done for a wide variety of books, and other media.
They did later lift some of those blocks after everyone stopped sharing the video of the shootings, but not all of them. (And if the government ordered blocks on some of those, I actually would be fairly comfortable with it, if it were done with process and transparency.)
This isn't a judgement of whether their actions were morally right or wrong. However, an ISP should probably be pre-emptively calling MPs to make a decision, rather than controlling access directly.
I have no idea what legal mechanisms the US govt has to pursue something like this, nor am I a user of TikTok, so I may be speaking from a point of ignorance here.
Even explicitly hostile foreign outlets like RT and PressTV should be protected by freedom of speech.
1) Declare TikTok a foreign media organisation, subject to controls.
2) Impose a trade duty on such apps or require some kind of minimum pricing (nobody would download it if it cost $2)
3) Declare government subsidy of Bytedance anti-competitive under trade rules and sanction the product.
4) Explore the boundaries of an Executive Order.
Etc. etc.