Can I refile my 2019 federal without claiming one of my dependent's?

You can prepare an amended return for 2019 to remove a dependent.  If you are doing that so that the dependent can get stimulus money, do not bother.  If you are not claiming that dependent on your 2020 return they can file a 2020 return and get the stimulus money by using the Recovery Rebate Credit on their own tax return.

If you need to remove the dependent for some other reason:

https://ttlc.intuit.com/questions/2566895-what-does-it-mean-to-amend-a-return

https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed?jump_to=answer_3288565

It takes 4-6 months for the IRS to process an amended return.

No you cannot "re-file" but you can amend to remove a dependent that you were not entitled to claim.

Why do you want to remove the dependent?  

(If so the dependent can claim the stimulus then the dependent cannot claim it if they *could* be a dependent whether actually claimed or not.  The IRS no longer issues stimulus based on prior tax reruns - only for new 2020 tax returns  now.)

Amended returns take about 6 months to process.

there is no requirement to claim a dependent. nevertheless, on the dependent's return, they must mark yes if the COULD be claimed as a dependent.