Terahertz pulse imaging of cutaneous malignant melanoma dehydrated by ethanol and embedded in paraffin was carried out across a frequency range of 0.2–1.4 THz. First, the tissue images based on the time-domain electric-field amplitude information were acquired. Then the areas of normal and cancerous tissues were determined using multi-scale, multi-azimuth and multi-structural element mathematical morphology. The physical meaning of the image was analyzed by calculation of the refractive index and absorption coefficient of cutaneous malignant melanoma in different areas. The refractive index of both normal and cancerous tissues showed anomalous dispersion. The refractive index of cancerous tissues tended to vary between 0.2 and 0.7 THz, while that of normal and fat tissues remain almost unchanged. The absorption of cancerous tissues was higher, with a maximum at 0.37 THz. We concluded that both the refractive index and absorption coefficient differ considerably between normal and cancerous tissues, and the areas of normal and abnormal tissues can be identified using THz pulse imaging combined with mathematical morphology. The method for edge detection of terahertz pulse imaging of cutaneous malignant melanoma provides a reference for the safe surgical removal of malignant tumors.