Can water itself be counted as a mutanajjis? For example, my nail was bleeding, and some water got under the nail and then trickled onto the back of my hand. Thus, will the water that touched the blood be first mutanajjis and then the back of my hand where the water touched second mutanajjis?
The criterion for considering something a first mutanajjis is that it came into contact with the najasah directly. Therefore, in the example you mentioned, the water that came into contact with the blood under your nail is the first mutanajjis. As for the back of your hand, if the water that came into contact with it has not itself contacted a najasah, it is pure. However, if the water came into contact with a najasah, like the blood under the nail (as above), the back of your hand would then be a second mutanajjis.