Electromechanical coupling in complex oxide heterostructures opens new possibilities for the development of a broad range of novel electronic devices with enhanced functionality. In this article, the switchable hysteretic electromechanical behavior of crystalline epitaxial LaAlO3 (LAO) thin films associated with polarization induced by electrical and mechanical stimuli is investigated. The field-time-dependent testing of the induced polarization states along with transport measurements and theoretical modeling suggests that the ferroelectric-like response of the LAO thin films is mediated by the field-induced ion migration in the bulk of the film. Comparative analysis of the dynamics of polarization reversal under the electrical field and mechanical stress applied via a tip of a scanning probe microscope demonstrates that both electrical and mechanical stimulus can be used to effectively control polarization at least at the submillisecond timescale. However, the mechanical writing is more localized than the electrical one. A combined electrical/mechanical approach for tuning the physical properties of oxide heterostructures may potentially facilitate novel memory and logic devices, in which the data bits are written mechanically and read electrically.