The invention discloses a novel tube and bar rolled piece sawing device and a sawing method thereof. According to the method, lifting baffles and pressing devices are arranged symmetrically about a saw blade. Novel lifting baffle devices are used for stopping moving tubes and bars during production of the tubes and the bars, are symmetrically arranged on two sides of a sawing machine generally and cooperate with the sawing machine and the pressing devices to saw heads and tails of the tubes and the bars, space can be saved, lengths of sawed stub bars of the heads or the tails of the tubes and the bars are within 20 mm, and problems that the stub bars are too long and difficult to collect are solved. The method is used for sawing the heads, the tails and specified lengths of the tubes and the bars and is a novel sawing method for short stub bars and fixed lengths, the lengths of the sawed stub bars of the heads or the tails of the tubes and the bars can be controlled within 20 mm, and the sawing quality is good.