Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena, and their promising applications in a new generation of spintronic devices take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected, and annihilated. In this work our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the transient creation and propagation of topological singularities (magnetic monopolelike Bloch points). Critically, our results predict that during the winding/unwinding of skyrmionic textures, the Bloch-point propagation will give rise to an emergent electric field with a substantial amplitude and in the terahertz frequency range. We also demonstrate ways for controlling Bloch-point dynamics, which directly enable the tunablility on generation of this signal, as well as its frequency and amplitude. Our studies provide a concept of directly exploiting topological singularities for terahertz skyrmion-based electronic devices.