When you swat an insect, do you see a fountain of red blood smeared on your hand? Not unless you've killed a full mosquito. Bug goo is generally green-blue, and that can tell us something about why fictional species might have green blood.
The divergence between humans and insects is as apparent on the inside as it is on the outside. They are without the internal structures we take for granted. For example, they don't have what we could consider to be blood vessels. Instead, blood moves through the hollow spaces in their body and is usually pumped not by a heart, but by a long central tube.
The blood they have is also different from our own. It's green. This color isn't arbitrary. Our blood is red because the hemoglobin which carries oxygen around uses iron, which turns reddish when oxygenated. Insects have hemocyanin, which serves the same purpose, but uses copper to transport oxygen instead of iron. What color does copper turn when it's exposed to oxygen? When an insects blood is not oxygenated, it's a nondescript gray. When it is oxygenated, it's a green-blue.
The difference between insect blood and our own is based on the fundamental elements in the blood, not incidental ones. This means that other species (even fictional species) which have green blood might have it for the same reason insects do - their blood oxygenation system is based on copper, not iron. That's a weakness. Copper isn't as efficient a carrier as iron. Many of the giant insects of earlier eras lived at times of higher oxygenation. Once the oxygen level of the planet dropped they smothered. So, if you have to fight a green-blooded Vulcan, and you know you can't best him by strength, try turning down the oxygen level, or meet him at a high altitude, where oxygen is scarce. It will weaken both of you, but it should weaken him more.