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I know I can do it, but should I? Is there a kinder way to communicate it? (apart from “quickly”) What happened when you did it?
Airbnb took a nearly 3 week booking (6 weeks away) for about 70-100% less than every other host due to wonky configuration of a “smart” pricing tool 
YOU took an IB booking without being on top of your pricing. Most folks here will tell you to bite the bullet and take the booking and learn from your mistake. However, only you can decide if you want to communicate with the guest or not and raise the rates. It’s a huge hit. Can you afford to host for 3 weeks at that rate? Are you a newbie host and need to stack your reviews and should only allow 7 day stays at the most?
I would turn off smart pricing (it seems to be the cause of these issues more often than not) right away.
I can afford it, first time I’ve considered it in 6 years of hosting. I’m just curious how other people have handled communication with guests, or if I’m risking more than bad karma.
I’m using Beyond Pricing (not Airbnb smart) fwiw.
How much do you value your honor/integrity over money?
Be aware that if you cancel, the dates will be blocked by Airbnb, so the only way to fill them is with bookings from another platform.
You do know that 100% less than something actually zero, right? 
There are several posts on this forum about this particular topic. I would say that practically 100% of hosts say suck it up and learn from it. I couldn’t afford a 70% loss on the room in my home for 3 weeks, so I’d just have to find a diplomatic way to say “not possible” and hope I didn’t get dinged by AirBnB.
I don’t know what Beyond Pricing is, but apparently it’s not working!! 
I’m glad you addressed this. I didn’t even want to go there… 
I meant market prices are 70-100 percent more than mine for those days
Some will agree with me and others will not. You certainly did not intend for this to happen. When you “set things up” you had an understanding of what the pricing would be - and got caught by surprise afterward.
Every mistake as a host does not “need to be honored with you losing a lot of money”. You are running a business and things will happen on occasion.
I would first set min/max smart pricing to proper levels. Then call airbnb to cancel the 3 week booking (“we are very uncomfortable with this guest”). Then, set the multi-calendar to have proper pricing for weekends / special days / etc for that time-frame.
I would not “eat $1000 or more” just because some other hosts on a forum do not agree with how I would choose to rectify an honest mistake.
Just make sure that you are on top of your game from now on, so that it does not happen again. If you allow this to happen again, it is negligence, mis-management, and not just an honest mistake and issues with using the booking system.
Oh, these situations always stink.
If it were a 3-day holiday weekend you forgot to premium price, I’d say suck it up and pay the “idiot tax”.
But on a 3 week booking that massive discount is pretty hard to absorb. I think I’d use one of my 3 Insta-book cancellations and get it cancelled penalty-free.
THIS. It’s always a learning experience. You have 5 years (?) under your belt as a host. If this is a one-off, then do what @Jefferson suggests and cancel penalty-free and raise your rates.
But get your pricing straight.
If it’s not a one-off, you might want to look at the mistakes you’re making. I’ve made a couple of doozies lately and I want to hide under the pool cover…
If it’s someone else’s fault, i.e. Airbnb’s fault or Beyond Pricing’s fault, then talk to them. If it’s their responsibility and you can prove it, then demand that they put the situation right.
I’ve never used Beyond Pricing but I’ve used Airbnb’s Smart Pricing for years and it has never been ‘wonky’. The only way it could be would be if I manually set erroneous prices after a few gins or something. Are you really sure that this was a wonky pricing tool? Really truly? Then talk to them.
Yeah I’m not gonna argue, and they charge 1% of gross.
Thanks for the fast feedback everyone. It’s the right decision for me to cancel given the booking is 6 weeks away, and I fixed the prices.
Thankfully this isn’t correct (for this cancellation anyway) - my listing is available again on Airbnb at the new rates.
Did you cancel with the reason “I am uncomfortable with this guest?”
Yes - though I was clear to Airbnb & the guest that I’d made a mistake with pricing.
To my surprise, the ex-guest sent back an understanding message!