In a medium bowl, combine tuna, olives, olive oil, capers, parsley, mustard and salt and stir to combine.
Lay out 6 slices of bread and divide tuna mixture between each slice, spreading across in an even layer. Top each with 6 slices of radish and top with remaining slices of bread.
Press down lightly to secure. Cut in half at a diagonal to form 2 triangle sandwiches. Can be made up to 2 hours in advance if wrapped tightly in plastic wrap and refrigerated.