By mistake, I withdrew my RMD twice and now I am in a higher and punishing tax bracket. Anything I can do to reduce my RMD to what it should be?

You did not take the RMD twice.   You took the RMD once and also took a distribution in excess of the RMD which could be returned to the IRA as a rollover IF returned within 60 days of the distribution.  So if you took it in December then you might still be within the 60 day window.

Unfortunately, if over 60 days then it will just be a taxable distribution that cannot be returned.

Maybe.  If it has been sixty (60) days or less since you took the more recent distribution, you may be able to return it using the sixty-day "rollover" rule - if you didn't have any other rollovers in the prior year.   

The rollover rules can get a little complicated, and I don't have all of the information I would need to be sure that this would work in your case, but it can't hurt to try! 

If you think this applies in your case, reach out to your bank or financial adviser for assistance.  For indirect rollovers, as this would be, the burden of proof falls on you, so be sure to keep things such as copies of deposit slips or tracking numbers, etc. to show that deadlines were met.

Your case may be even more likely to generate a request for information from the IRS since the distribution and rollover would be in two different tax years. Don't let that discourage you from taking advantage of this opportunity if you qualify for it, though. Just keep good records!