Mesoscopic superpositions of distinguishable coherent states provide an analogue of the 'Schrodinger's cat' thought experiment(1,2). For mechanical oscillators these have primarily been realized using coherent wavepackets, for which the distinguishability arises as a result of the spatial separation of the superposed states(3-5). Here we demonstrate superpositions composed of squeezed wavepackets, which we generate by applying an internal-state-dependent force to a single trapped ion initialized in a squeezed vacuum state with nine decibel reduction in the quadrature variance. This allows us to characterize the initial squeezed wavepacket by monitoring the onset of spin-motion entanglement, and to verify the evolution of the number states of the oscillator as a function of the duration of the force. In both cases we observe clear differences between displacements aligned with the squeezed and anti-squeezed axes. We observe coherent revivals when inverting the state-dependent force after separating the wavepackets by more than 19 times the ground-state root mean squared extent, which corresponds to 56 times the root mean squared extent of the squeezed wavepacket along the displacement direction. Aside from their fundamental nature, these states may be useful for quantum metrology(6) or quantum information processing with continuous variables(7-9).