Yes! The superstition goes that if you break a mirror, the first thing you are to do is immediately cover it. The key is not to let the tiny fragments catch your image. It was believed to "split" your spirit/soul causing damage. If you already looked into them, the only way to "release" the parts of you "trapped" in the mirror is to smash the mirror bits into tinier little pieces, as tiny as possible! Dust even! So that no image can be viewed from them. Then the pieces can be buried.
If you do so, please be sure to wrap the glass securely in a cloth you will be disposing with it (old t-shirt for example) so that the shards cannot fly up into your face when you smash them with a hammer or mallet. Best to do it outdoors too. You don't want a sliver to sneak out and step on it.
Of course this is all a part of belief and if you believe it is bad luck, then it is! And if you believe it can cause damage, then it can. And if you believe breaking the mirror into even tinier pieces will fix it all, then it will.
This is actual old time superstition recorded down in ye olde English back in the day when it wasn't scoffed at like it is today. Every superstition had a reversal. Like throwing salt over your left shoulder after spilling it. Or mixing salt into pepper that has been spilled before disposing it. These ideas of how to counter such things are handy.
I love reading books on superstition. You tend to find a lot of old folklore and magick goodies that way which most people have forgotten. ;)