Arrange the bread slices on a clean work surface. Spread each slice with some of the mayonnaise, then spread 4 of the slices with the mustard.
Arrange the liverwurst on the mustard-coated bread slices. Drape the cucumber over the liverwurst. Sprinkle with the caraway seeds, then top with the remaining slices of bread, mayonnaise-side down.
Using a serrated knife, trim the crusts. Slice each sandwich in half before serving.