I think it's clear that she's saying both.
On the one hand, her uses of "desu" (the Japanese copula, sort of like English "be") are all as part of syntactically-acceptable sentences. But she uses the word a fair bit more than a typical speaker of Japanese would, often using it in constructions where a typical speaker would more likely omit it or choose a different locution.
On the other hand, the curious way she stresses the word whenever she says it suggests that she's "punning" it with English "death", which is also written "desu" in Japanese. Further, if you look at the lyrics for her character songs ("DoomsDay's Dogma" from "Kagayaki no Fantastic Stage" and "Dark Death Decoration" from "Dark Iris Musical Grammar"), you'll note that her uses of "desu" are written in katakana (デス). The most common use of katakana is to represent loanwords. (I also note that "DoomsDay's Dogma" reveals a strong preoccupation with English words beginning with the letter "D", the most obvious of which [in this context] is "death".)
Obviously, this pun-like-thing doesn't work in English, so if you're subtitling her speech, a generous dollop of "death" in her speech is a reasonable workaround.