Make the blackberry base: Mash the blackberries, mint and sugar in a medium bowl with a fork to make a chunky sauce. Let stand until very juicy, about 30 minutes. (You should have about 1 cup blackberry base, enough for 4 cocktails.)
For each drink: Combine 1/4 cup of the blackberry base and the sherry in a shaker filled with ice and shake well. Strain into a tall glass filled with crushed ice. Garnish with blackberries.