Background: Recent theoretical and experimental researches using proton-induced $alpha$-knockout reactions provide direct manifestation of $alpha$-cluster formation in nuclei. In recent and future experiments, $alpha$-knockout data are available for neutron-rich beryllium isotopes. In $^{12}$Be , rich phenomena are induced by the formation of $alpha$-clusters surrounded by neutrons, for instance, breaking of the neutron magic number $N=8$. Purpose: Our objective is to provide direct probing of the $alpha$-cluster formation in the $^{12}$Be target through associating the structure information obtained by a microscopic theory with the experimental observables of $alpha$-knockout reactions. Method: We formulate a new wave function of the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) type for the structure calculation of ${}^{12}$Be nucleus and integrate it with the distorted wave impulse approximation framework for the $alpha$-knockout reaction calculation of $^{12}$Be$(p,palpha)^{8}$He. Results: We reproduce the low-lying spectrum of the $^{12}$Be nucleus using the THSR wave function and discuss the cluster structure of the ground state. Based on the microscopic wave function, the optical potentials and $alpha$-cluster wave function are determined and utilized in the calculation of ${}^{12}$Be($p,palpha$)${}^{8}$He reaction at 250 MeV. The possibility of probing the clustering state of $^{12}$Be through this reaction is demonstrated by analysis of the triple differential cross sections that are sensitively dependent on the $alpha$-cluster amplitude at the nuclear surface. Conclusions: This study provides a feasible approach to validate directly the theoretical predictions of clustering features in the $^{12}$Be nucleus through the $alpha$-knockout reaction.
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