As a promising biofabrication technology, extrusion-based bioprinting has gained significant attention in the last decade and major advances have been made in the development of bioinks. However, suitable synthetic and stimuli-responsive bioinks are underrepresented in this context. In this work, we described a hybrid system of nanoclay Laponite XLG and thermoresponsive block copolymer poly(2-methyl-2-oxazoline)-b-poly(2-n-propyl-2-oxazine) (PMeOx-b-PnPrOzi) as a novel biomaterial ink and discussed its critical properties relevant for extrusion-based bioprinting, including viscoelastic properties and printability. The hybrid hydrogel retains the thermogelling properties but is strengthened by the added clay (over 5 kPa of storage modulus and 240 Pa of yield stress). Importantly, the shear-thinning character is further enhanced, which, in combination with very rapid viscosity recovery (similar to 1 s) and structure recovery (similar to 10 s), is highly beneficial for extrusion-based 3D printing. Accordingly, various 3D patterns could be printed with markedly enhanced resolution and shape fidelity compared to the biomaterial ink without added clay. Graphic abstract