Deformation twinning in crystals is a highly coherent inelastic shearing process that controls the mechanical behaviour of many materials, but its origin and spatio-temporal features are shrouded in mystery. Using micro-compression and in situ nano-compression experiments, here we find that the stress required for deformation twinning increases drastically with decreasing sample size of a titanium alloy single crystal, until the sample size is reduced to one micrometre, below which the deformation twinning is entirely replaced by less correlated, ordinary dislocation plasticity. Accompanying the transition in deformation mechanism, the maximum flow stress of the submicrometre-sized pillars was observed to saturate at a value close to titanium's ideal strength. We develop a 'stimulated slip' model to explain the strong size dependence of deformation twinning. The sample size in transition is relatively large and easily accessible in experiments, making our understanding of size dependence relevant for applications.