Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Ibn ‘Abbas (may Allah be pleased with them both) reported that the Prophet (peace and blessings be upon him) said: “Healing is to be found in three things: drinking honey, the knife of the cupper, and cauterization of fire.” (Al-Bukhari)
According to a hadith narrated by Jabir (may Allah be pleased with him), the Prophet (peace and blessings be upon him) said: “If there is any good in your medical treatments, it is in the knife of the cupper, drinking honey, or cauterization with fire, as appropriate to the cause of the illness, but I would not like to be cauterized.” (Al-Bukhari)
Answering your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
This issue is contentious among scholars. One group considers it as one of the things that break the fast, while others do not think so. The differences of opinion are due to the different reports attributed to the Prophet (peace be upon him) on this issue. He has been reported saying, “Both the one who practices blood- cupping and the one receiving it break their fasts.” On the other hand, Ibn `Abbas says that the Prophet (peace be upon him) did undergo blood-cupping while fasting.
The majority of scholars who allow the practice do so by relying on the reported practice of the Prophet and his Companions, as we know many used to undergo it while fasting.
This group considers the previous report as being abrogated.
While endorsing the majority view on this, some scholars have rightly said it would be better if one has a choice to postpone it until after iftar – especially if it leaves a person weak and unable to continue the fast. The same rule applies to donating blood while fasting.
Allah Almighty knows best.