The longer a blood stain is allowed to set, the more difficult it will be to remove. With carpet, the blood will seep down into the fibres underneath the surface, which will cause the stain to appear no matter how long or hard you scrub the carpet. With fabric, the blood stain will penetrate all fibres, especially once it's been allowed to coagulate. Even though most carpets are stain-resistant, you'll have a hard time removing dried and coagulated blood.
There are different methods to remove blood stains from carpet. But it is highly recommended to use the "gentlest" method first - Water Removal Method. If there is still visible blood stain after the process, try the other "stronger" methods.
It is easiest to remove blood when it is still wet. Dried blood stains are notoriously harder to remove. Also be sure throughout the process to blot the stain, not rub it, as this will only push the stain further into the carpet fibres. Use the following steps along with the appropriate carpet cleaning solution for your carpet type.
You should never use hot water to remove a blood stain from either carpet or fabric because the heat will speed the drying and setting process. Get a tub of cool or cold water and a clean sponge or rag, then lightly begin sponging the stain from the outermost edges to the centre of the stain. If you try to sponge outward, you can spread the stain, which will make it that much harder to remove.
Once you've sponged the blood stain carefully for several minutes, use a clean sponge or cloth to mop up the excess water. Again, make sure to use outer-to-inner strokes to avoid spreading what's left of the stain. If you are concerned about spreading it, you can always use a shop-vac or other suction device to dry the area. You should also avoid pressing down on the stain, as that will help to set it faster.
Continue repeating the cold water and drying until you can't get the sponge to bring any red out of the carpet or fabric. Make sure that you allow the water to dry thoroughly between each sponging. Let a fan blow over it or set a towel with something heavy on top of it. It doesn't matter whether the blood came from a bloody nose or a paper cut, blood stains are messy and no one wants to see a stain from blood on the carpet.