To meet the requirements of low-latency communication technology in the 6G terahertz band, porous alumina ceramics with ultra-low dielectric constant and directional pore channels were prepared by a freeze-drying method. A relationship between the structure and the properties of samples from different locations was investigated. The effect of solid content on the microstructure, mechanical properties, terahertz optical and dielectric properties was analyzed. Porous alumina ceramics with high porosity (i.e., 68.9%-81.0%) and compressive strength (i.e., 17.6-87.8 MPa) can be obtained, having ultra-low refractive index (i.e., 1.38-1.63), absorption coefficient (i.e., ~2.5 cm-1), dielectric constant (i.e., 1.90-2.67), and z dielectric loss (i.e., ~0.008) at 1 THz. The directional pore channels exhibit high compressive strength in the direction parallel to the pores, and the special structure has potential applications for terahertz waveguides and antenna substrates.