We demonstrate a fabrication scheme for clean suspended structures using chemical-vapor-deposition-grown graphene and a dry transfer method on lift-off-resist-coated substrates to facilitate suspended graphene nanoelectronic devices for technological applications. It encompasses the demands for scalable fabrication as well as for ultra-fast response due to weak coupling to environment. The fabricated devices exhibited initially a weak field-effect response with substantial positive (p) doping which transformed into weak negative (n) doping upon current annealing at the temperature of 4 K. With increased annealing current, n-doping gradually decreased while the Dirac peak position approached zero in gate voltage. An ultra-low residual charge density of 9 × 108 cm-2 and a mobility of 1.9 × 105 cm2 V-1 s-1 were observed. Our samples display clear Fabry-Pérot (FP) conductance oscillation which indicates ballistic electron transport. The spacings of the FP oscillations are found to depend on the charge density in a manner that agrees with theoretical modeling based on Klein tunneling of Dirac particles. The ultra-low residual charge, the FP oscillations with density dependent period, and the high mobility prove the excellent quality of our suspended graphene devices. Owing to its simplicity, scalability and robustness, this fabrication scheme enhances possibilities for production of suspended, high-quality, two-dimensional-material structures for novel electronic applications.