do you think there are backups in the throne of heroes?
There is...so to speak. All Servants summoned from the Throne of Heros are actually copies of the originals.
Even the Holy Grail lacks the power to summon a true Heroic Spirit, so the process is facilitated by summoning them into one of seven vessels prepared beforehand. The Greater Grail makes a copy using information from the "main body" of the Heroic Spirit, an "emanation", that returns to them as information, in the form of a soul, upon the death of the Servant. Disconnected from the "main body", they are able to know of the actions of the Servant through records, as if reading a book. Due to this, any Heroic Spirit summoned in multiple Holy Grail Wars will lack knowledge of previous summonings. The only exemption is King Arthur due to her unique circumstances.
Source: Servants - Nature (2nd paragraph)
However, you'll note that it says the only exception is King Arthur (Arturia). This is because she isn't a Heroic Spirit yet.
Before her last breath, she appealed to the world; in exchange for services as a Heroic Spirit, she asked to be given an opportunity seek the Holy Grail to save her country.
Source: Saber (Fate/Stay Night) - Profile - Identity - Downfall (2nd Paragraph)
What this means is that when Arturia is summoned she isn't being summoned from the Throne of Heroes, and instead is being summoned as a part of her deal with the world to seek the Holy Grail. It's for this reason why in the 5th Holy Grail War she had memories of the 4th War.
I can't find anything which indicates that a Counter Guardian is another exception but EMIYA seemed to believe he wasn't a clone.
Even knowing that the Throne of Heroes was isolated from time and space, Archer desperately came to believe that his only hope of release was to have himself summoned into an era where Shirou Emiya exists and kill his past self, hoping that the double paradox created by Shirou Emiya being killed before having a chance to make the contract with Alaya and that the killing was done by a Shirou Emiya who successfully made the contract with the world would create a time paradox great enough in magnitude that could potentially erase his existence as a Counter Guardian.
Source: Archer - Profile - Identity (4th paragraphg)
Of course, even if EMIYA wasn't a clone, his plan would still fail because he was in another timeline. Even if he killed a past version of himself, this would only deprive that reality of Shirou possibly becoming a Counter Guardian. I recall reading that in the timeline EMIYA came from, the 5th Holy Grail War did not end in any of the ways shown in the visual novel and that EMIYA witnessed The Shadow's destruction which is why in Heaven's Feel he abandons his plan to kill Shirou and instead returns to his former duty as a Counter Guardian in order to destroy The Shadow (which he comments he has seen before).
Also with your comment
Killing him, even with Shiki's MEoDP would only destroy his Grail-granted body
This is true. However, as I explain in this answer, which Shiki one refers to affects the likelihood of that Shiki being able to kill a Servant. Even when their Mystic Eyes allow them to kill a Servant, in the end it still comes down to combat ability. Tohno Shiki has problems maintaining his because of his migraines, and Ryougi Shiki can maintain an on-par level defensive fight.
[Ryougi Shiki's] combat ability is only possibly around the level of Ciel, allowing her to manage a defensive fight against a being on the level of a Servant. While still much stronger than [Tohno] Shiki, who holds no hope in even competing with a Servant defensively
the Mystic Eyes of Death Perception are only a slight advantage in scoring an instant death blow, the user still has to be able to fight (or atleast get in close) to beliver the attack
But as for "How can the counter guardians die?" outside the Holy Grail War this has yet to be seen since really the only Counter Guardian we see is EMIYA and this is in the form of a Servant.
considering that Counter Guardians are a Counter Force for Ayala, the collective unconsciousness of mankind and the drive for survival, one can assume that if they aren't being copied when they get summoned they can die but my only basis for this is because Counter Guardians were once human and thus do have a concept of death, as opposed to Aristoteles who don't have concepts of damage or death in which the Mystic Eyes of Death Perception wont work
Beings like Type Mercury and other Ultimate Ones lack the concept of death entirely, so the ability will not affect them under any circumstance.
Source: Mystic Eyes of Death Perception - Workings - Points (3rd paragraph)