This is pretty easy to do, and is covered well in articles such as this one. However, I made the mistake of powering down my machine after removing my bad drive from the array. My thinking was that it would be easier to perform the surgery this way. In retrospect I should have simply unmounted my array (so that there was a greater margin of error in pulling out a wrong cable, etc).
At any rate, the machine wouldn’t boot Ubuntu after taking the drive out of the array because of mdadm’s degraded state. I was able to finish this job while booting into Ubuntu’s recovery mode. Note that if you reboot while recovery is still in progress you’ll be faced with this same issue. The slight problem this presented was that my monitor wasn’t connected to my PC, making navigating into recovery mode difficult.