The symbiotic-like binary Mira and nova V407 Cyg was observed in outburst in 2010 March and monitored in several wavelength bands. The outburst had, to some extent, characteristics similar to those observed during other nova eruptions, such as that occurred recently in RS Oph and U Sco, suggesting that the blast wave interacted with the giant companion and propagated through a dense circumstellar medium enveloping the binary system. Here we report on multidimensional hydrodynamic simulations describing the 2010 outburst of V407 Cyg, exploring the first 60 d of evolution. The model takes into account thermal conduction (including the effects of heat flux saturation) and radiative cooling; the pre-explosion system conditions included the companion star and a circumbinary density enhancement that are believed to influence the evolution and morphology of the blast wave. The simulations showed that the blast and the ejecta distribution are both aspherical due to the inhomogeneous circumstellar medium in which they expand; in particular, they are significantly collimated in polar directions (producing a bipolar shock morphology) if the circumstellar envelope is characterized by an equatorial density enhancement. The blast is partially shielded by the Mira companion, producing a wake with dense and hot post-shock plasma on the rear side of the companion star; most of the X-ray emission produced during the evolution of the blast arises from this plasma structure. The observed X-ray light curve can be reproduced, assuming values of outburst energy and ejected mass similar to those of RS Oph and U Sco, if a circumbinary gas density enhancement is included in the model. In particular, our ‘best-fitting’ model predicts that the 2010 blast propagated through a circumbinary gas density enhancement with radius of the order of 40 au and gas density ≈106 cm−3 and that the mass of ejecta in the outburst was Mej≈ 2 × 10−7 M⊙ with an explosion energy E0≈ 2 × 1044 erg. Alternatively, the model can produce a similar X-ray light curve without the need of a circumbinary gas density enhancement only if the outburst energy and ejected mass were similar to those at the upper end of ranges for classical novae, namely Mej≈ 5 × 10−5 M⊙ and E0≈ 5 × 1046 erg.