To reset a project, it needs to be hit by an earthquake while it's being built. Even then it's often not reset so you might need to hit it more than once.

Since players don't get the earthquake power until very late in the game it is likely that all projects will have been finished by then, so you'll need to "save" a project only partially started well in advance, with the intention of hitting it with an earthquake when you can. WARNING: Make sure you don't have many (preferably any) builders checked, or you may find they've finished it without asking!