Blood is a body fluid in the circulatory system of vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood is a composition of blood cells suspended in blood plasma, which constitutes 55% of blood fluid, 92% of water and contains proteins, glucose, mineral ions, hormones, carbon dioxide. Albumin is the main protein in plasma, and it functions to regulate the colloidal osmotic pressure of blood.

Some animals, like crustaceans and mollusks, use haemocyanin to carry oxygen, replacement of hemoglobin. Some Insects have a fluid called hemolymph instead of blood, the difference is that hemolymph is not contained in a closed circulatory system. In most beings, this "blood" does not contain oxygen-carrying molecules like hemoglobin because their bodies are small enough for their tracheal system to sufficient oxygen supply.

RED

Hemoglobin is a protein contains iron which transport oxygen present in red blood cells built up from subunits containing ‘haems’. Almost all vertebrates as well as in some invertebrate animals. Their structure gives blood its red colour when oxygenated. Deoxygenated blood is a deep red colour. 

Hemoglobin in blood carries oxygen from the respiratory organs like lungs to the other tissues of the body, there it releases the oxygen to enable aerobic respiration which ignite the animal's metabolism. Hemoglobin is also a metalloprotein (which contain metal) and chromoprotein (which gives colour).

BLUE

Hemocyanins are proteins that transport oxygen throughout the bodies of some invertebrate animals like spiders, octopuses, squids and some molluscs. These metalloproteins contains 2 copper atoms instead of one iron that reversibly bind with a single oxygen molecule (O2). They are second frequently use oxygen transport molecule after hemoglobin by nature. 

Unlike the hemoglobin in red blood cells found in vertebrates, which is bound to red blood cells, haemocyanin floats free in the hemolymph (blood). When deoxygenated, the blood is colourless by Cu(I) complex , but when oxygenated, it gives a blue colouration by Cu(II) complex formation.

GREEN

Chlorocruorin is Chemically similar to haemoglobin some species contains both haemoglobin & chlorocruorin in their blood. Erythrocruorin which is similar to chlorocruorin are large oxygen-carrying hemeproteins Both are sometimes called as giant hemoglobin. 

They are found in Some Segmented worms, leeches, marine worms, Some lizards, annelids and arthropods (including some insects). It is particularly found in certain marine polychaetes. Chlorocruorin has a weaker affinity for oxygen than hemoglobin. Chlorocruorin is a dichromatic compound noted for appearing green in dilute solutions, it appears light red in concentrated solutions.

This enormous macromolecule is typically found free floating in the plasma, and not contained within red blood cells. When deoxygenated it turns to light green, when oxygenated it becomes green, although when more concentrated it appears light red.

VIOLET

Hemerythrin is an oligomeric protein (simple repeating group of monomers) responsible for oxygen (O2) transport in the marine invertebrate phyla of Sipuncula, Peanut worms, Penis worms, brachiopods and Magelona. 

When compared to haemoglobin, Haemerythrin is only 1/4 as efficient at oxygen transport. Myohemerythrin is a monomeric O2-binding protein found in marine invertebrates. Hemerythrin and myohemerythrin are colourless In deoxygenated state, but it imparts a violet-pink colour when oxygenated.

Reference:

1) https://www.medicalnewstoday.com/articles/321442

2) https://en.wikipedia.org/wiki/Green_blood

3) https://www.vox.com/xpress/2014/10/31/7133779/blood-blue-green-purple

4) https://animals.howstuffworks.com/animal-facts/5-animals-whose-blood-isnt-red.htm