The method and device for cutting fresh tissue slices utilizes a vibrating microtome. The vibrating microtome uses a cutting blade that vibrates in a horizontal direction. The microtome has a base, a specimen holder attached to the base, and a diagonal slide carriage and support arm that are supported on the base for movement diagonally with respect to the specimen holder. A vibrating blade support is located on the support arm and moves horizontally with respect to the specimen holder. A cutting blade is mounted on the vibrating blade support and moves in a compound diagonal and vibrating motion with respect to the specimen holder.