To make the beet infused sake, combine cubed beets and sake and let sit for 1 hour. Strain and store in a sealed container.
To make the punch, muddle the chili in a pitcher and add the beet infused sake, simple syrup, lime juice, and sherry. Refrigerate until ready to serve, up to 4 hours.
To serve, combine the punch base with ginger beer in an ice filled pitcher or punch bowl.