We have developed a novel detector, referred to as an $alpha$-ToF detector, for correlated measurements of atomic masses and decay properties of low-yield, short-lived radioactive isotopes using a multi-reflection time-of-flight mass spectrograph. By correlating measured time-of-flight signals with decay events, it will be possible to suppress background events and obtain accurate, high-precision mass values even in cases of very low event rates. An offline test of the $alpha$-ToF detector has shown that the time-of-flight detection efficiency for 5.48~MeV $alpha$-rays is more than 90% and yields a time resolution of 251.5(68)~ps and an energy resolution of 141.1(9)~keV. Using a two-dimensional spectrum of the correlated $alpha$-ray energy and time-of-flight, the $alpha$-rays from mixed $alpha$ sources could be fairly well resolved.