The　numerical　manifold　method　(NMM)　has　been　widely　utilized　to　solve　problems　involving　complicated　boundaries,　cracks,　and　interfaces.　Recently,　strain　or　gradient　smoothing　techniques　have　been　incorporated　into　NMM　to　improve　its　performance.　The　resulting　smoothed　NMMs　(SNMMs)　normally　possess　enhanced　numerical　properties,　for　example,　higher　accuracy,　convergence,　and　efficiency.　A　challenging　issue　rooted　in　NMM　and　other　enhanced　finite　element　methods　using　unfitted　meshes　is　the　ill-conditioning　induced　by　extremely　small　cut　element.　In　this　study,　we　investigate　the　behaviors　of　SNMMs　in　the　case　of　small　cut　element.　It　is　demonstrated　that　the　cut-induced　ill-conditionings　also　exist　for　two　types　of　SNMMs,　namely,　edge-based　SNMM　and　physical-patch-based　SNMM.　Furthermore,　a　preconditioner　based　on　the　normalization　of　basis　functions　is　proposed　to　resolve　the　ill-conditioning.　Several　benchmark　problems　demonstrate　the　performances　of　SNMMs　regarding　accuracy,　convergence,　and　stability.