Sequence-specific endonuclease Cas12-based biosensors have rapidly evolved as a strong tool to detect nucleic acids. Magnetic particles (MPs) with attached DNA structures could be used as a universal platform to manipulate the DNA-cleavage activity of Cas12. Here, we propose nanostructures of trans- and cis-DNA targets immobilized on the MPs. The main advantage of the nanostructures is a rigid double-stranded DNA adaptor that distances the cleavage site from the MP surface to ensure maximum Cas12 activity. Adaptors with different lengths were compared by detecting the cleavage by fluorescence and gel electrophoresis of the released DNA fragments. The length-dependent effects for cleavage on the MPs’ surface were found both for cis- and trans-targets. For trans-DNA targets with a cleavable 15-dT tail, the results showed that the optimal range of the adaptor length was 120–300 bp. For cis-targets, we varied the length and location of the adaptor (at the PAM or spacer ends) to estimate the effect of the MP’s surface on the PAM-recognition process or R-loop formation. The sequential arrangement of an adaptor, PAM, and a spacer was preferred and required the minimum adaptor length of 3 bp. Thus, with cis-cleavage, the cleavage site can be located closer to the surface of the MPs than with trans-cleavage. The findings provide solutions for efficient Cas12-based biosensors using surface-attached DNA structures.