Preheat sandwich press. Slice bread into 8 thick pieces. Slice strawberries and cucumber.
Butter the outside of each slice of bread. Spread cream cheese on the inside of 4 slices. Add chopped or sliced mint and sliced strawberries. Top with remaining 4 slices of bread.
Heat sandwiches for 2-3 minutes per side or until golden brown.
Serve with leftover strawberries and cucumber slices on the side.