Use the Invert audio effect for negating unwanted sounds.
Sometimes passers by cough, sneeze, clap...stuff you really don't want to hear. Copy an audio clip, after seperating from the video, into a new audio track. Match frame to the first but trim it to right before and after the sound. Select the new track and drag the Invert Effect on it. Unwanted sound should now be gone.
If I understand correctly, you are making a copy of the unwanted sound and subtracting it from the original. Why not just turn the sound down, eg with keying or cutting the audio and deleting?. X-X is the same as 0.
If there is also general background noise present, you will hear a break in the background noise with all methods.
In this case I go further and copy some similar background noise from nearby and fill the silence with it. If the noise was copied from only a short distance away, it is best to reverse the audio to avoid the sound sounding repetitive.