The effect of quasi-continuous (QC) equal-channel angular pressing (ECAP) in various pre-aged states on the structure formation and mechanical and functional properties of a hyper-equiatomic titanium nickelide (TiNi) shape memory alloy is studied. QC ECAP with a channel intersection angle of 110° is carried out at a temperature of 450 °C after aging for 1 and 5 h for three passes. To investigate the obtained structure and properties, the following research methods are applied: transmission electron microscopy, XRD analysis, calorimetric study, tension and hardness tests, and a special technique for the determination of functional properties. QC ECAP allows for the considerable refinement of structural elements and results in obtaining a mixed fine-grade structure, with structural elements of average sizes of 92 nm after pre-aging for 1 h and 115 nm after pre-aging for 5 h. Pre-aging for 5 h before QC ECAP, in combination with QC ECAP and post-deformation aging at 430 °C for 1 h, provides the best combination of mechanical and functional properties: a dislocation yield stress of 1410 MPa, ultimate tensile strength of 1562 MPa, and total recoverable strain of 11.6%. These values are comparable with the best results obtained for titanium nickelide and expand opportunities for the application of smart shape memory devices.