Recent observations of destructive quantum interference in single-molecule junctions confirm the role of quantum effects in the electronic conductance properties of molecular systems. These effects are central to a broad range of chemical and biological processes and may be beneficial for the design of single-molecule electronic components to exploit the intrinsic quantum effects that occur at the molecular scale. Here we show that destructive interference can be turned on or off within the same molecular system by mechanically controlling its conformation. Using a combination of ab initio calculations and single-molecule conductance measurements, we demonstrate the existence of a quasiperiodic destructive quantum-interference pattern along the breaking traces of π-stacked molecular dimers. The results demonstrate that it is possible to control the molecular conductance over more than one order of magnitude and with a sub-ångström resolution by exploiting the subtle structure-property relationship of π-stacked dimers.