The dissociation dynamics of HD⁺ molecule in an intense field is investigated by using an accurate three-dimensional time-dependent wave packet approach. When the 790-nm laser pulse interacts with HD⁺ molecule, the lowest electronic 1sσ and 2pσ states are coupled. Due to the existence of the permanent electric dipole moment, the transitions in HD⁺ molecule involve the direct absorption of an odd and even number of photons, thereby opening different pathways for dissociation. The model of the photon-dressed states is presented to analyze the possible dissociation pathways of HD⁺ molecule. The laser-induced dissociation of HD⁺ molecule is mainly composed of the four pathways: the direct one-photon absorption, the net two-photon absorption, the direct two-photon absorption, and the direct two-photon absorption. To reveal the dissociation mechanism of HD⁺ molecule, the kinetic energy resolved spectra are calculated at the given laser intensities. It is found that the dissociation pathways are strongly dependent on laser intensity, especially for the net one-photon absorption dissociation and direct two-photon absorption dissociation. With further research, the dissociation pathways of HD⁺ are controlled by regulating the intensity of laser pulse. At a laser intensity of 4.0 × 10¹³ W/cm², the kinetic energy resolved spectrum for the vibrational state ν = 3 includes the contributions from the net two-photon absorption dissociation and the direct two-photon absorption dissociation. For the vibrational state ν = 6, HD⁺ molecule is preferentially dissociated via the net one-photon absorption. However, the dissociation mechanism of HD⁺ molecule at the vibrational states ν = 3 and ν = 6 have significant changes as the laser intensity increases to 2.0 × 10¹⁴ W/cm². For the vibrational state ν = 3, the branching ratio between the dissociation pathway of the net two-photon absorption and that of the direct two-photon absorption has a dramatic change with the increase of laser intensity. Compared with the kinetic energy resolved spectra at laser energy of 4.0 × 10¹³ W/cm², the height of the dissociation peak from the net two-photon absorption decreases, and that of the direct two-photon absorption increases at laser intensity of 2.0 × 10¹⁴ W/cm². For the vibrational state ν = 6, the dissociation process of the net one-photon absorption almost disappears at laser intensity of 2.0 × 10¹⁴ W/cm², and it is replaced by the dissociation pathway of the direct two-photon absorption.