Yes, there are differences. Here are the examples:
排除 usually be used in an investigative topic.
eg.
1 - 排除故障, remove the error from the device.
2 - Let's put this suspect A aside(排除嫌疑犯A), focusing our efforts on seeking suspect B and C in downtown Manhattan area! (集中精力搜寻嫌疑犯B和C)
解除 A verb, similar to cancel.
eg.
1 - The blackout is canceled (宵禁被解除了)
2 - Your amazon order has been canceled. (你的amazon订单被解除了)
3 - Your employment contract has been canceled. (你的雇佣合同被解除了)