The narrative exemplifies that the Pain summons are alive, though. I mean, Asura Path is displayed to exude blood (Kakashi's Raikiri) implying it possesses an advanced intricately designed biological system which implies that it could die of blood loss, severe damage to internal organs, splitting of the arteries and veins. The term used to reference thier revival is
revitalization instead of
repair implying life. They are composed of organic tissue enriched with chakra through the rods. The fact that they have to utilize hand seals (ie., molding chakra requires concious effort supplied by the chakra circulatory pathways) implies that they possess an intricate chakra pathway system. It might not instantly dispel but that boils down to the properties of the offense involved. Kisame states that his blade cuts things to
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implying it conflates with the definition of an ordinary knife like exemplified in the scan which implies that it can reduce the centipede to significantly smaller parts with rapid fire successive slashes.
If he has to resummon it, the creature has to be in definite congruent shape (fit for battle simulations) which is impossible seeing as it would be divided into ribbons. If he tries to repair it'd consume a significant amount of time, implying that it'd be practically useless as it's an autowin due to BFR. Although he can technically repair it's virtually impossible to gauge the amount of time the process would consume.
I don't think that they are immortal tbf. The whole reason why they were hyped like immortals were explicitly due to the fact that they had this whole secret behind thier function ie., get killed, get revived or repair damage acquired and blindside the opponent who believes they won the battle. They aren't literally immortal, although they possess pseudo-immortality like Kakuzu and Hidan.
How would it biologically operate though, having it's body parts cut to ribbons? There is the additional risk of having it's chakra sapped which likely weakens or exhausts it significantly. It doesn't have any technique that could be streamed from the mouth if I recall.
If we presume it's composed of chakra wouldn't that implicate that characters with chakra absorption would effectively circumvent it's physique? I mean, if Samehada absorbed six tails chakra worth that implicates that it would've partly erased a bijuu if not completely (6-1) if it had been in close proximity, implying that Samehada is suddenly a bijuu subjugater which directly contradicts it's portrayal and features. We have no explicit evidence on whether sapping a literal manifested bijuu is possible. It hasn't been implied or exemplified.
Sakura possesses significantly superior physical power compared to Samehada however I see it more of as a battle of offensive attrition (ie., the centipede can only block a limited number of ribbon cutting slashes while Kisame has the features that alludes to him being capable of avoiding the centipede's assaults physically while dealing assaults concurrently.) that definitely wears out the summon. The blade is pretty durable - it tanked Killer Bee's V2 Lariat partially implying that likely translates to it's offensive power in some way shape or form. It lacking any notable offensive features implies it wouldn't put Kisame down indefinitely.