Topological magnons offer unique opportunities for low-dissipation spin transport, but achieving nonvolatile control over their topological states remains a significant challenge. Here, using a Heisenberg-Dzyaloshinskii-Moriya model and symmetry analysis, we propose a ferroelectrically tunable magnonic platform that enables reversible switching among three distinct topological phases: a second-order topological magnon insulator, a topological magnon insulator, and a normal magnon insulator. This transition is characterized by the simultaneous emergence and reversal of spontaneous magnon valley polarization. We further identify the ${\mathrm{Ti}}_3{\mathrm{I}}_8$ monolayer with a breathing kagome lattice as a promising material platform that supports electric-field-driven topological switching and reversal of spontaneous magnon valley polarization, as confirmed by first-principles calculations. Notably, this material platform also hosts electrically controllable valley-dependent magnonic transport, including valley Hall and valley Nernst effects. This Letter establishes topological magnons as a functional bridge linking ferroelectricity with magnon cornertronic and magnon valleytronic responses.

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• Magnons
• Topological insulators
• Valley degrees of freedom
• Multiferroics
• Density functional theory
• First-principles calculations
• Heisenberg model
• Spin wave theory