As a novel terahertz (THz) source, a spintronic THz emitter (STE) has become a research hot topic recently due to its ultra-broadband emission, powerful scalability, simple fabrication, and ultrawide pump-wavelength range. To optimize the performance of a STE, its spintronic heterostructure has been extensively investigated and its accessories have been also appropriately improved. In this work, a curved substrate of a STE was proposed and utilized to achieve the modulation of the THz wave front as a new degree of freedom. A STE with a neutral-meniscus substrate was designed and fabricated to attain the focusing function of the emitted THz radiation. Coaxial THz bi-focus with a non-overlapping spatio-temporal distribution were effectively generated and applied in multi-plane imaging by properly using two cascade STEs. Amplitude- and phase-type objects consisting of bilayer structures were measured by the scheme. The focused and defocused regions of the samples were distinguished and analyzed on different cross sections. Furthermore, a STE with a spiral stair substrate was manufactured in this way and the generation of a THz vortex beam was fulfilled. The convenient approach offered more possibilities for developing THz optospintronic devices.