Mirrors are made up of two parts, the glass and then a reflective coating on the back. Because of this, they are not considered 100% glass and many times the town's recycle pickup (if your have one) for glass will not take them because there will be an additional process to separate the glass from the reflective material backing.
Possible disposal methods:
- Throw it out. We have a recycling/trash center in our town and for a
fee you can dispose of bulk items that the trash guys will not pick
up. A mirror of that size would be considered a bulk item.
- Recycle. Check your local recycling center, some of them will
recycle mirrors at no cost.
- Repurpose. The mirror could be reused by someone else as is if it is
good shape. Some advertisement may be necessary in local media, or you can use free advertising as indicated below in the comments by @Steve.
- Donate. A mirror or especially a broken mirror can be reused for
many arts and crafts type projects like a mosiac. Check with
schools/university or with any local artisans, they might take it off
Finally, in thier spare time one could create a funkadelic disco ball from the mirror and then sell it on eBay for a small profit.