Cassava production generates significant amounts of by-products such as leaves and tuber peel. Instead of considering them as waste, valorization aims to find sustainable ways to utilize them. However, the presence of cyanide and insoluble fibers poses a major obstacle to their conversion into valuable products. Therefore, the objective of this study is to investigate the changes in cyanide concentration and quality of cassava leaves after mechanical pressing and in tuber peel after treatment with an enzyme solution. Frozen leaves were screw-pressed into their fractions: juice, and press cake. The results show that the cyanide level in the press cake was reduced to 73.56% and was concentrated by 97.48% in the juice compared to the frozen leaves. However, the crude protein values of the frozen leaves, juice, and press cake did not differ significantly (p > 0.05), and were 27.09%, 25.47%, and 23.82%, respectively. In addition, the results for the peel revealed that pretreatment with Viscozyme® L, which assists in the mechanical peeling of cassava tubers, also contributed to a reduction in cyanide and insoluble fiber in the peel. Cyanide content was lowered by 53.89–58.94% in enzyme-treated peel from all three runs (ETP1-3) when compared to fresh peel (FP), while the reduction was only 8.63% in the control peel (CP) treated with hot water without enzyme solution. The insoluble fibers in cassava peel, such as neutral detergent fiber (NDF), acid detergent fiber (ADF), acid detergent lignin (ADL), and crude fiber (CF), were also degraded more effectively after treatment with an enzyme solution than with hot water.