Answered by Ustadh Tabraze Azam
Question: I often get chapped lips where blood comes (but it does not flow). I dab the blood with a tissue paper. According to this definition it does not break wudu (because it must flow on its own)? Does dabbing it with a tissue make any difference?
Answer: Wa alaikum assalam wa rahmatullahi wa barakatuh,
I pray that you are in the best of health and faith, insha’Allah.
No, dabbing and clearing away such blood is not considered “flow” and would not affect the ruling.
According to the Hanafi school, blood which flows (beyond the point of exit)  actually or  effectively (such that it would have flowed had it not been wiped/absorbed away) invalidates the ablution (wudu). [Shurunbulali, Maraqi al-Falah; `Ala al-Din `Abidin, al-Hadiyya al-`Ala’iyya]
And Allah alone gives success.
Checked & Approved by Faraz Rabbani