If the you that is now is not the you that you were a moment ago, as some would suggest, then we are being duplicated and discarded between moments anyway, and what is the difference between that and the duplicate being deferred to a spacetime point dislocated by some sort of transmat method, rather than merely practically adjacent in Planck-spacetime coordinates by the operation of the universe?
The nature of the 'death' of the precursor could be as violent (or as experienceless) as any artificial disposal method of the clonee body, we don't and (spiritualism aside, which is probably otherwise incompatible for several establishable reasons) unknowable by any and all successor copies, as the new "now"s and new "here"s have no knowledge of that part of either the old "now" or the old "here" self(s).
Feel free to suggest a possible scientific test, but until then I suspect the metaphysics involved is just so much pure philosophy.
(On the topic of duplication/cloning by Transporter technology, there's a book I read, many decades hence, where an entanglement phenomenon was used for practical purposes. With either two transportation clones from the same clonee, or by retaining the clonee, momentarily upon use of the device an existential link was maintained between both individuals, until outside influences shook them 'apart'. But by keeping (or by placing in-situ) one in a sensory deprivation environment, the experiential link was maintained, up until the severing of the link (e.g. the ambulatory version's death), at which point the copy could be released, to report and upon their "twin"'s actions. Experiencing one's own death 'first hand', and then potentially going back into the same situation with knowledge of how to avoid it, was a traumatic experience, but there was one particularly resilient individual who was being used to explore a "fatal death trap puzzle" alien space-ship, learning by iterative (re)incarnations that within a certain corridor it was fatal to step into the green-lit areas, or that turning hatch handles clockwise during certain periods of time (or failing to do so during all other times) was bad for ones corporeality. And so was gradually trying to reach through the various (sometimes literal!) pitfalls, often past his prior corpse(s)... It was very much like a modern FPS with go-again-from-checkpoint plus persistent-player-corpses features, except written at least a decade before even DOOM (maybe more).... And obviously, as a fictional conceit, bears little connection to practical physics (e.g., isn't being entombed within a sensory deprivation environment itself a sensory discrimination sufficient to collapse the spooky-experience-at-a-distance experiential-waveform) and only really matters to the book plot, but I thought I should mention it as a kind of thought experiment.)