A trailer-mounted pipe-handling apparatus has an elongate cradle swivelable about a longitudinal swivel axis for loading or offloading pipe at a well site. With the cradle horizontal, and swiveled into a loading position, loading arms receive a pipe from a loading rack, whereupon kicker members move the pipe from the loading arms into the cradle. With the cradle swiveled into a neutral position supporting the pipe, a swing arm raises one end of the cradle while simultaneously drawing its other end horizontally along a base track, thus placing the cradle in a tilted configuration. The raised end of the pipe can thus be positioned above the floor of a drilling rig or service rig for connection to the rig hoist, which can then lift the pipe out of the cradle. Pipe may be removed from the well using a similar, reverse procedure. The rig hoist positions a removed pipe in the tiltingly elevated cradle, which is then lowered to the horizontal position. The cradle is then swiveled to an offloading position, allowing the pipe to roll out of the cradle onto an offload rack.