Mirror modifier

I’m trying to use the mirror modifier to model a house but I have a problem.

I want to add a chimney on one side of the house, I tried deleting the mirror modifier but it removes the other side. Is there any way to temporarily stop the mirror modifier and then start it again without the chimney to be added on the other side too and without the other side to be deleted?

The mirror modifier does exactly as its name suggests. It creates a mirrored object. Both the original and mirrored side will be the same (as in a mirror). If you want them different you will need to apply the modifier first them adjust the object without the modifier or just add the chimney as a separate object.