Microfluidics have transformed diagnosis and screening in regenerative medicine. Recently, they are showing much promise in biofabrication. However, their adoption is inhibited by costly and drawn-out lithographic processes thus limiting progress. Here, multi-material fibers with complex core-shell geometries with sizes matching those of human arteries and arterioles are fabricated employing versatile microfluidic devices produced using an agile and inexpensive manufacturing pipeline. The pipeline consists of material extrusion additive manufacturing with an innovative continuously varied extrusion (CONVEX) approach to produce microfluidics with complex seamless geometries including, novel variable-width zigzag (V-zigzag) mixers with channel widths ranging from 100–400 µm and hydrodynamic flow-focusing components. The microfluidic systems facilitated rapid mixing of fluids by decelerating the fluids at specific zones to allow for increased diffusion across the interfaces. Better mixing even at high flow rates (100−1000 µL min −1) whilst avoiding turbulence led to high cell cytocompatibility (>86%) even when 100 µm nozzles are used. The presented 3D-printed microfluidic system is versatile, simple and efficient, offering a great potential to significantly advance the microfluidic platform in regenerative medicine.