Exploiting relays in millimeter wave (mmWave) systems is an effective way to extend the communication coverage and overcome the blockage problem. This paper comprehensively studies secure transmissions in mmWave decode-and-forward (DF) relay systems. Depending on the overlapped resolvable paths between the main channel and the wiretap channel in each transmission stage, we consider three eavesdropping scenarios, namely two-stage eavesdropping (TSE), single-stage eavesdropping (SSE) and no eavesdropping (NE). We investigate secrecy performance and optimal parameter design of these eavesdropping scenarios under the same codeword transmission (SCT) scheme and the different codewords transmission (DCT) scheme, where source and relay utilize same codeword or different codewords. Specifically, we derive closed-form expressions for connection probability and secrecy outage probability, and then give solution to the secrecy throughput maximization problem. Furthermore, we investigate the effectiveness of the artificial noise (AN) by evaluating the secrecy performance of AN assisted transmissions. Numerical results are provided to verify our theoretical analysis. Our results give insights into the secure transmission scheme selection and the impact of various parameters, such as number of antennas, power allocation between source and relay, number of overlapped paths, and distances between different nodes, on the secrecy performance of the mmWave relay system.