Due to the low price and good comprehensive properties, FRP composite material has become a new type of civil application material in recent years. In this paper, Araldite® 2012 adhesive was used to bond basalt-fiber-reinforced polymer (BFRP), and the durability of its bonded joints was investigated. Experiments were carried out at 80 °C/DI water (deionized water), 80 °C/3.5% NaCl solution (3.5% SS), and 80 °C/5.0% NaCl solution (5.0% SS) at 0- (unaged), 10-, 20-, and 30-day aging. The specimen and BFRP in the environment of 80 °C/DI water, 80 °C/3.5% SS, and 80 °C/5.0% SS found salt solution under the condition of all sample water absorption decreases, and the activity of salt solution chemistry was weaker compared with deionized water. The load–displacement curve of the joint failure was obtained through quasi-static tensile experiments, and it was found that the adhesive would undergo a post-curing reaction that had a positive impact on the stiffness of the joint in a high-temperature environment. At the same time, it was found that the joint failure strength decreased less in the salt solution environment, and deionized water was more destructive than the salt solution. Referring to the change in water absorption, it was found that the change in the mechanical properties of the joint was mainly related to the permeation effect of the polymer. The change in the Tg of adhesive was measured by differential scanning calorimetry (DSC). It was found that Tg would decrease after aging, and the change in Tg was mainly related to the mobility of the molecular chain. Thermogravimetric analysis (TGA) was used to analyze the thermal behavior of the epoxy resin and some organic matter, and the main weight loss stage was 340–450 °C, which was the complete degradation of epoxy resin and some organic matter. Macro visual and microscopic scanning electron microscope (SEM) and energy dispersive X-ray spectroscopy (EDX) were used to analyze the failure section, and it can be concluded that the failure mode of joint tear failure transitioned to cohesion in the late–mixed interface failure, at the visible interface between the fiber and the resin matrix.