Terrific question! In fact, many commentaries have addressed this seeming incongruity in their writings: If the breaking of the glass is to recall the destruction, why is it followed by such an outbreak of joy? Some have written that, at a minimum, people have become confused, thinking that the breaking of the glass is itself a joyous custom. Others have even written that the custom of saying mazal tov at the breaking is a mistake in the first place. One great rabbi even went so far as to write that he would nullify it if he could.
Nevertheless, saying mazal tov immediately after breaking the glass is a widespread and accepted practice in all communities I’m familiar with. So how can we reconcile these two “polar opposites”?
A basic way to explain is that once the glass has been broken, the Temple has been recalled, and at that point the simcha (happy occasion) should continue in a joyous manner. The people who are present therefore kick off this joy with the heartfelt blessing of mazal tov!
I’ve heard a deeper meaning to explain saying mazal tov after breaking the glass, based on an idea from the Rozhiner Rebbe. The Talmud states that when a man and woman marry in a kosher way, the Divine Presence dwells in their midst. One name of God, spelled yud and heh, is the product of the only differences between spellings of the Hebrew words for man and woman. The main name of God, however, also called the Tetragrammaton, is spelled with two added letters: vav and heh. When we take the word chupah and subtract from it the word pach (i.e., vessel, which in this case refers to the broken glass), we remain with two more letters: vav and heh. Adding these to the initial yud and heh forms the complete, ineffable four-letter name of God. When that happens at the chupah it is a jubilant time, and certainly a time to wish the bride and groom a hearty mazal tov!
I’ve heard another explanation, which is meant to be lighthearted: When the groom steps on the glass, it symbolizes the “last time” that he will put his foot down. Not only is this a positive omen for the bride, but also for the groom, since from now on they will act as one unit in harmony.
