They still haven't discarded visas for them. (so they still need them to travel to some countries)

They still haven't done away with visas for them.

Is it OK to use either "discard" or "do away"?

Discard means to throw away, to put in the trash bin.
I discarded the old files because I didn't need them anymore. I did not discard my recent records.
Do away with means to stop producing. It is not natural or fluent English in this case.
It is better to say:
They stopped producing travel visas for many countries when the regulations were relaxed.
They continue to produce travel visas for some countries because it is still required by law.

Let's say that the South Koreans do not need to apply for a visa to travel to the US, so the visas for the South Koreans have been ........ (what?)

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"discontinued" That is the first word that comes to mind.

So if I wanted to say the reverse would it be OK: The visas for the South Koreans are still continued.

Does it work this way?
Hi guys,

It's not really the visas so much as the need for visas that is being discussed. I'd accept this.

The US still hasn't discarded / done away with / dispensed with the need/requirement for Koreans to have visas.

Or other ways, eg The US still requires Koreans to have visas.

Best wishes, Clive
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Thanks guys. Now it's clear.
Thanks Clive for getting to the real issue.