The invention discloses a method for the pervaporation and vapor-permeation separation of a gas-liquid mixture or a liquid mixture by a SAPO-34 molecular sieve membrane prepared in a dry gel process, comprising: 1) synthesis of SAPO-34 molecular sieve seeds; 2) coating the SAPO-34 seeds on a porous support; 3) preparation of a mother liquor for dry gel synthesis of SAPO-34 molecular sieve membrane; 4) supporting the mother liquor for dry gel synthesis on the porous support coated with SAPO molecular sieve seeds and drying; 5) placing the porous support prepared in step 4) into a reaction vessel, adding a solvent, performing crystallization of the dry gel; 6) calcining; 7) using the SAPO-34 molecular sieve membrane obtained from step 6) to perform separation of a gas-liquid mixture or a liquid mixture by a process of pervaporation separation or vapor-permeation separation. The invention has the advantages of very high methanol selectivity and permeation flux, lowering synthesis cost of molecular sieve membrane and lowering environment pollution.