normally, consuming anything invalidates the fast. So I would avoid eating tissues or biting it out.
The guidelines concerning the blood that invalidates the fast are as follows:
1 – If the blood comes out as the result of a person’s actions or choice; this is subject to further discussion:
(i) If the blood comes out by means of cupping, this invalidates the fast, because the Prophet (peace and blessings of Allaah be upon him) said: “The cupper and the one to whom cupping is done both break their fast.”
(ii) If it comes out by a means other than cupping, such as venesection (opening a vein). If the amount is large and that has an effect on the person’s body, then this invalidates his fast (such as donating blood). If the amount is small and it does not harm the person, then it does not invalidate his fast, such as the small amount of blood that is taken for testing.