Remove seeds and chop the cucumbers very fine. Let sit in a strainer over a bowl for 15-20 minutes so some of the water comes out. Press with paper towel to remove extra water.
Combine cucumbers, cream cheese, lime juice, and mint leaves in a serving bowl, until well blended. Add salt and pepper to taste. If desired, add a little mayonnaise to produce a spreading consistency.
Spread by tablespoonfuls on little party rye bread slices and top with another slice. Using a 2 1/2-inch biscuit cutter, cut each sandwich into a round shape if desired. Or, cut in half diagonally to make small triangles.