First-principles density functional theory (DFT) is used to reveal bonding differences between two types of nanotube deformation: (1) tubes bent under mechanical duress, and (2) tubes pushed by atomically sharp AFM tips. Bent tubes maintain an all-hexagonal network up to large bending angles. In contrast, AFM-probed tubes, even for the smallest deformations, develop an inward cone-like structure terminating in an apex. Progressively more pushing results in sp(3)-coordination of the C-atom at the apex, followed by spontaneous bond-rupture. Dangling-bond defects in the middle of the tube explain orders of magnitude decrease in the electrical conductance of AFM-probed tubes.