This study leverages the advantages of two fabrication techniques, namely, melt-extrusion-based 3D printing and porogen leaching, to develop multiphasic scaffolds with controllable properties essential for scaffold-guided dental tissue regeneration. Polycaprolactone–salt composites are 3D-printed and salt microparticles within the scaffold struts are leached out, revealing a network of microporosity. Extensive characterization confirms that multiscale scaffolds are highly tuneable in terms of their mechanical properties, degradation kinetics, and surface morphology. It can be seen that the surface roughness of the polycaprolactone scaffolds (9.41 ± 3.01 µm) increases with porogen leaching and the use of larger porogens lead to higher roughness values, reaching 28.75 ± 7.48 µm. Multiscale scaffolds exhibit improved attachment and proliferation of 3T3 fibroblast cells as well as extracellular matrix production, compared with their single-scale counterparts (an approximate 1.5- to 2-fold increase in cellular viability and metabolic activity), suggesting that these structures could potentially lead to improved tissue regeneration due to their favourable and reproducible surface morphology. Finally, various scaffolds designed as a drug delivery device were explored by loading them with the antibiotic drug cefazolin. These studies show that by using a multiphasic scaffold design, a sustained drug release profile can be achieved. The combined results strongly support the further development of these scaffolds for dental tissue regeneration applications.