Canada
The Currency Act states that "no person shall melt down, break up or use otherwise than as currency any coin that is legal tender in Canada." Similarly, Section 456 of The Criminal Code of Canada says: "Every one who (a) defaces a current coin, or (b) utters a current coin that has been defaced, is guilty of an offence punishable on summary conviction."
However neither the Currency Act nor Criminal Code mention paper currency. It therefore remains legal to completely destroy paper currency.