Revealing the interaction mechanisms between anticancer drugs and target DNA molecules at the single-molecule level is a hot research topic in the interdisciplinary fields of biophysical chemistry and pharmaceutical engineering. When fluorescence imaging technology is employed to carry out this kind of research, a knotty problem due to fluorescent dye molecules and drug molecules acting on a DNA molecule simultaneously is encountered. In this paper, based on self-made novel solid active substrates NpAA/(ZnO-ZnCl2)/AuNPs, we use a surface-enhanced Raman spectroscopy method, inverted fluorescence microscope technology, and a molecular docking method to investigate the action of the fluorescent dye YOYO-1 and the drug DOX on calf thymus DNA (ctDNA) molecules and the influencing effects and competitive relationships of YOYO-1 on the binding properties of the ctDNA-DOX complex. The interaction sites and modes of action between the YOYO-1 and the ctDNA-DOX complex are systematically examined, and the DOX with the ctDNA-YOYO-1 are compared, and the impact of YOYO-1 on the stability of the ctDNA-DOX complex and the competitive mechanism between DOX and YOYO-1 acting with DNA molecules are elucidated. This study has helpful experimental guidance and a theoretical foundation to expound the mechanism of interaction between drugs and biomolecules at the single-molecule level.