To obtain the shear capacity calculation method and competition failure mechanism of headed stud connectors of steel–concrete composite structures under the influence of freeze–thaw cycles (FTCs) and artificial corrosion (AC), the material performance of concrete specimens after the FTCs and push-out tests of 36 headed stud connectors specimens were tested under the influence of FTCs and AC. The cubic compressive strength, dynamic elastic modulus, and mass loss rate of C50 concrete were obtained under different FTCs. Failure modes, load-slip curve, shear capacity, and shear stiffness of stud connectors were investigated based on push-out tests of miniaturized specimens. Based on the nonlinear fitting of test data, a formula for calculating the shear capacity reduction factor is proposed. Results show that the shear capacity and stiffness of stud connectors will deteriorate due to the deterioration of concrete performance caused by FTCs or the weakening of stud section caused by AC. The two failure modes of stud breakage or concrete cracking will change with the aggravation of FTCs and AC effect.