While they may bleed and take damage to their organs, their true being resides in a Spiritual Core they obtain upon first materializing. Their Material Body envelopes it, and damage must be inflicted to it in order for them to be defeated. It gradually diminishes under magical energy expenditure and while sustaining bodily damage, and their expenditure will escalate under such conditions. If it is damaged through powerful magical energy, curses, or Noble Phantasms, it will be destroyed, meaning that the Servant can no longer stay materialized. The heart and head are directly connected to it, so they are a Servant's greatest weaknesses. Sustaining damage will significantly weaken it, with some Servants having it instantly destroyed and some with skills like Battle Continuation being able to at least temporarily sustain themselves.
Fate/complete material III: World material - Record of Heavens Feel - Servant System: How to Defeat A Servant, p.018
Basically, you can't injure the Spiritual Core without attacking the Material Body. By being unable to injure the Spiritual Core, you can't do damage to a Servant.
TL:DR: I'm right, you're wrong, Nasu makes the rules, follow them.
