By dropping the "of" the reading of that sentence changes the verb "dispose" from intransitive to transitive, which gives it a different denotative meaning. The transitive form of "dispose" means "to organize" or "to give an inclination toward something". So the sentence would read "Toronto uses landfill for organizing about three-quaters of its waste", following standard grammar rules.
However, I think the context around the verb does a lot of the heavy lifting for supplying meaning. When talking about landfill and waste, the "get rid of" meaning of "dispose" seems intuitive, even if the grammar does not support that meaning according to accepted definitions of the word.