The present disclosure relates to a cut ring assembly including a backup member, an intermediate member and a cutting ring body.The intermediate member is formed of a thin, rigid material that is sandwiched between the backup member and the cutting ring body. The thin, rigid material is formed of a material having a hardness less than the hardness of the backup member and greater than the hardness of the cutting ring body. The present disclosure also relates to an anvil assembly including such a cut ring assembly.