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The ability to create stimuli-responsive DNA nanostructures has played a prominent role in dynamic DNA nanotechnology. Primary among these is the process of toehold-based strand displacement, where a nucleic acid molecule can act as a trigger to cause conformational changes in custom-designed DNA nanostructures. Here, we add another layer of control to strand displacement reactions through a 'toehold clipping' process. By designing DNA complexes with a photocleavable linker-containing toehold or an RNA toehold, we show that we can use light (UV) or enzyme (ribonuclease) to eliminate the toehold, thus preventing strand displacement reactions. We use molecular dynamics simulations to analyze the structural effects of incorporating a photocleavable linker in DNA complexes. Beyond simple DNA duplexes, we also demonstrate the toehold clipping process in a model DNA nanostructure, by designing a toehold containing double-bundle DNA tetrahedron that disassembles when an invading strand is added, but stays intact after the toehold clipping process even in the presence of the invading strand. This work is an example of combining multiple physical or molecular stimuli to provide additional remote control over DNA nanostructure reconfiguration, advances that hold potential use in biosensing, drug delivery or molecular computation.