What you are trying to do should work just fine, assuming that the static network settings are correct.
I have here a GRV-R7-MM1001-10 and it is powered over PoE on ETH1. It has a static IP address. On ETH0 I have my PC connected using a Static IP address. All works fine and my PC can even access the Internet via the switched Ethernet interfaces in the groov RIO.
Perhaps double check the network configuration at your Yokogawa device.