To synthesize high quality (co)polyesters derived from 2,5-furandicarboxylic acid (FA), an acetic acid refluxing/pH-swing method was proposed to purify FA. 2-Carboxyl furfural and other impurities were removed completely from FA with this method. Using highly purified FA, biobased polyester poly(butylene furnadicarboxylate) (PBF) and aliphatic-aromatic copolyesters poly(butylene adipate-co-butylene 2,5-furandicarboxy-late)s (PBAFs) were synthesized via melt (co)polycondensation. The (co)polyesters were characterized with GPC, FTIR, ¹H NMR, DSC and TGA, and their tensile mechanical properties were also assessed. The copolyesters possess random chain structure, monomer feed ratio-controlled copolymer composition and excellent thermal stability (T_d,5% > 340 ^oC) in full composition range. Both BA-rich and BF-rich PBAFs are crystalline polymers. The crystallizability decreases with composition, up to nearly amorphous at moderate ?_BF (40-60%). PBAFs with ?_BF no more than 50% exhibit obvious high-elastic deformation and rebound resilience, and possess tensile properties (E 18-160 MPa, s_b 9-17 MPa, e_b 370-910%) comparable to poly(butylene adipate). PBAFs with higher ?_BF behave like nonrigid plastics with low tensile moduli (42-110 MPa), moderate strength (30-42 MPa) and high elongation at break (310-470%). In comparison, PBF is a strong and tough thermoplastic having balanced mechanical properties, namely, much higher tensile modulus (1.9 GPa) and strength (56 MPa) and high elongation at break (260%). It seems necessary and effective to use highly purified FA for synthesizing high performance FA-derived (co)polyesters.