I often catch blood from the rabbits as I'm bleeding them out. I use it in for both the garden and for culinary use. Catching blood from an animal that's hanging while bleeding out is a simple task, and I never skip doing anything that's simple to do!
When catching the blood for culinary use, I employ all the tricks I can to get as much useful blood as possible. I start with two nesting bowls. The bottom bowl is full of ice cubes and the top bowl that I use for catching the blood is sitting on top of the ice cubes. Whenever the catching bowl is not in use, it's sitting on top of the ice cubes, keeping it ice cold. I add 1-2 tbsp of vinegar to the catching bowl as the acidic vinegar is going to help to keep the blood from coagulating before it can cool. I also keep a whisk in the catching bowl that's staying nice and cold, I use it to slowly stir the blood as it's being caught in the bowl, keeping it moving also helps to stop it from coagulating.
After a rabbit has fully bled out into the catching bowl, I continue to slowly stir the blood with the whisk until the blood is refrigerator cold to the touch... which I can feel when I put my finger in the blood. When it's cold enough I stop stirring and put the catching bowl back on top of the bowl with the ice, which keeps the blood very cold throughout the butchering process.
Once I'm done catching the last blood from the last rabbit, and cooling it down, I take the time to pour the blood through a small, fine mesh strainer into a clean jar. Putting the lid on the jar, I walk it into the house and refrigerate it immediately as blood has a short shelf life and will start to coagulate if if gets warm. Fresh blood will hold for 72 hours in the fridge, if you can't use it before then you can freeze it for later use.
I catch and cool the blood from one animal at a time, even when it's a small amount. When I catch the blood in the bowl, I use the whisk to keep it moving. It's a slow stirring, you want it to move but you want to minimalism any foaming.
When the blood has cooled to refrigerator temperature, you can quit stirring and strain it into a waiting container. Straining will remove any bits that may have clotted.
Once the blood is in the container, a canning jar in this case, I walk it into the house and put it in the refrigerator. Blood will store for about 72 hours when refrigerated. It's best to use it fresh when making sausages and pasta, but if you can't get to it for processing within 2 days of catching it, you can freeze it for later use.