A broadband and narrowband switchable terahertz (THz) absorber based on a bulk Dirac semimetal (BDS) and strontium titanate (STO) is proposed. Narrowband and broadband absorption can be switched by adjusting the Fermi level of the BDS. When the Fermi level of the BDS is 100meV, the device is an absorber with three narrowband absorption peaks. The frequencies are 0.44, 0.86, and 1.96THz, respectively, when the temperature of STO is 250K. By adjusting the temperature of STO from 250 to 500K, the blue shifts of the frequencies are approximately 0.14, 0.32, and 0.60THz, respectively. The sensitivities of the three absorption peaks are 0.56, 1.27, and 2.38GHz/K, respectively. When the Fermi level of the BDS is adjusted from 100 to 30meV, the device can be switched to a broadband absorber with a bandwidth of 0.70THz. By adjusting the temperature of STO from 250 to 500K, the central frequency shifts from 1.40 to 1.79THz, and the bandwidth broadens from 0.70 to 0.96THz. The sensitivity of the central frequency is 1.57GHz/K. The absorber also has a wide range of potential applications in multifunctional tunable devices, such as temperature sensors, stealth equipment, and filters.