(Abridged) The symbiotic-like binary Mira and nova V407 Cyg was observed in outburst on March 2010 and monitored in several wavelength bands. Here we report on multi-dimensional hydrodynamic simulations describing the 2010 outburst of V407 Cyg, exploring the first 60 days of evolution. The model takes into account thermal conduction and radiative cooling; the pre-explosion system conditions included the companion star and a circumbinary density enhancement. 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 lightcurve 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 this case, the 2010 blast propagated through a circumbinary gas density enhancement with radius of the order of 40 AU and gas density approx 10^6 cm^{-3} and the mass of ejecta in the outburst was M_{ej} approx 2times 10^{-7} M_{odot} with an explosion energy E_{0} approx 2times 10^{44} erg. Alternatively, the model can produce a similar X-ray lightcurve 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 M_{ej} approx 5times 10^{-5} M_{odot} and E_{0} approx 5times 10^{46} erg.
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