Magnetic transitions and magnetoresistance of HfFe6Ge6-type Y1-xDyxMn6Sn6 (x = 0.2 and 0.3) have been investigated in the temperature range of 5-380 K. It was found that the strong exchange interaction between the Dy and Mn sublattices results in incomplete ferromagnetism at Iow temperatures. At higher temperatures, the metamagnetic transition from an antiferromagnetic state to a ferrimagnetic state can be induced by a fairly small threshold field or by increasing temperature. The magnetic transition is accompanied by a large magnetoresistance effect of about -29% and -16% at 5 K for x = 0.2 and 0.3, respectively.