Combine sugar and water in a small saucepan over medium-low heat. Stir sugar until dissolved.
Add cloves and cinnamon sticks and simmer over low heat for 30 minutes.
Remove from heat and let cool. Strain cloves and cinnamon sticks from the syrup and refrigerate (syrup keeps in refrigerator for up to 2 weeks).
Combine vodka, blood orange juice, and syrup in a cocktail shaker filled with ice. Shake vigorously for 15 seconds. Strain liquid into a cocktail glass and garnish with a blood orange slice.