Reductive amination of 2,5-diformylfuran (DFF) was used to implement the transition from bio-derived 5-hydroxymethylfurfural (HMF) to pharmaceuticals. The synthesized bis(aminomethyl)furans were utilized as building blocks for the construction of new derivatives with structural cores of naturally occurring biologically active compounds. Using the one-pot procedure, which included the Diels–Alder reaction followed by hydrogenation of the double bond, bio-derived analogues of the anticancer drug norcantharidin were obtained. The cyclization process was diastereoselective, and resulted in the formation of tricyclic products with the endo configuration. Analysis of cytotoxycity for the resulting tricyclic amine-containing compounds showed an increase of anticancer activity as compared with the unsubstituted norcantharimide.