If you right click the pig you dismount it.
I have done it multiple times without fail, it isn't a "sometimes it works" kind of thing.
Dismounting does not work in water. Most likely because you ride a squid in water.
This glitch is most likely due to the fact that in vanilla minecraft you can dismount a pig with a saddle by right clicking it.
EDIT: Just tested more with piggify, It doesn't interrupt casts, it only delays them. So When I use chant, I heal when piggify ends, instead of being stopped from casting chant.