According to StillTasty.com, beetroot can be frozen. However, it is best to cook beetroot, and then freeze it. Beetroots can be frozen for up to 18 months when stored properly.
Before storing beetroots, wash them and trim the tops, leaving half an inch of stem. Cook the beets in boiling water until they are tender. Drain the beets, and let them cool. Remove the stems, and peel the beets. Quarter the beets, or place them whole in an airtight container or freezer bag. Beetroot freezes the best and stays fresh the longest when placed in a very cold freezer. Another option is placing beetroot at the back of the freezer.