Nucleic acids have been used to create diverse synthetic structural and dynamic systems. Toehold-mediated strand displacement has enabled the construction of sophisticated circuits, motors, and molecular computers. Yet it remains challenging to demonstrate complex structural reconfiguration in which a structure changes from a starting shape to another arbitrarily prescribed shape. To address this challenge, we have developed a general structural-reconfiguration method that utilizes the modularly interconnected architecture of single-stranded DNA tile and brick structures. The removal of one component strand reveals a newly exposed toehold on a neighboring strand, thus enabling us to remove regions of connected component strands without the need to modify the strands with predesigned external toeholds. By using this method, we reconfigured a two-dimensional rectangular DNA canvas into diverse prescribed shapes. We also used this method to reconfigure a three-dimensional DNA cuboid.