Different blood colours are caused by different proteins and pigments that are found in the blood. Such proteins will serve different purposes for the mammal that contains them to survive in different conditions such as below freezing point or other conditions.
One of the proteins that gives some mammals blue blood colour is the proteins called hemocyanin derived from copper. If proteins had higher levels of iron then their blood colour will turn into red colour.
Colour of the blood is also based on the oxygen levels that are present in the blood. Blood that contains oxidized copper proteins and the blood is oxygenated it turns blue. If blood is not oxygenated then it is colourless.
Some species that have blue blood are:
Horseshoe Crabs
The horseshow crabs have light blue blood, due to the high levels of copper protein in its blood. Because of the high levels of copper protein in the blood, horseshoe crabs have high levels of resistance to bacteria, and it is one of the reasons why it has survived for more than 400 million years.
Spiders
Spiders also have light blue blood colour because of the high levels of hemocyanin (copper protein) in the blood.
Scorpions
Some scorpions, especially the largest species of scorpions, have light blue blood. Also such types of scorpions have high levels of hemocyanin in the blood.