Assuming that this is setup so that the same sound is coming through both microphones just one with your voice on top, you could theoretically do this just by feeding it through something that inverts the polarity of the "to be cancelled out" sound and overlays the two sounds. I'm sure it wouldn't be perfect but you might be able to tune it to properly do it. This is how a active noise cancelling works!
Thank you for the idea. I've tried in the past to do something similar but couldn't get it right. I did try to rely on ideas from ANC but my domain knowledge is very lacking. It's been over 2 years since so I might need to give it another chance and see if any off the shelf library/product has been released since then.
That doesn’t work though, the requirement for the timing to align waveform by waveform is too high, and the speed of sound is too slow. Also the frequency response isn’t going to match exactly.
