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We perform two-dimensional hydrodynamic simulations for the thermonuclear explosion of Chandrasekhar-mass white dwarfs with dark matter (DM) cores in Newtonian gravity. We include a 19-isotope nuclear reaction network and make use of the pure turbulent deflagration model as the explosion mechanism in our simulations. Our numerical results show that the general properties of the explosion depend quite sensitively on the mass of the DM core MDM: a larger MDM generally leads to a weaker explosion and a lower mass of synthesized iron-peaked elements. In particular, the total mass of produced can drop from about 0.3 to 0.03 M⊙ as MDM increases from 0.01 to 0.03 M⊙. We have also constructed the bolometric light curves obtained from our simulations and found that our results match well with the observational data of sub-luminous Type Ia supernovae. [ABSTRACT FROM AUTHOR]