Although classified information cannot "through gross negligence be removed from its proper place of storage" (according to U.S. Code 793 f), legal precedent doesn't allow indictment for gross negligence – only for "intent." However, even when the words "through gross negligence" are replaced with "intentionally" in the aforementioned statute, the secretary is still indictable, assuming she knew about the presence of classified information. If she knew there was classified information and removed it, that's an intentional removal of classified information (from State Department servers to her private basement server), thus satisfying the precedent for prosecution under U.S. Code 793 f.
Proving intent in this fashion requires the single assumption that she knew there was classified information on her server. It would certainly be useful information to find out whether it's common knowledge among senators and congressmen that email communication occasionally contains classified information. Ostensibly, at the time of Ms. Clinton's appointment to secretary of state, the former two-term senator and Armed Services Committee member knew she would have a high volume of emails that occasionally contained some classified information (even a single sentence), yet she chose to have this information "removed from its proper place of custody" (a felony under 793 f) and "retained at an unauthorized location" (a misdemeanor under 1924 a).
The critical issue is whether she was aware of classified information – indeed, it's impossible for her to have intent to remove classified information if she didn't know the information was classified to begin with. That's why it was imperative for the secretary to say, "There was no classified information" when first confronted with the allegations on 3/10/15, while also claiming repeated amnesia and a janitor's understanding of classified information when interviewed by the FBI. Unfortunately for her, the instant she admits to knowing there was classified information, she's indictable for knowingly removing it – that's an intentional removal, not accidental (negligence).
In response to the charge that she mishandled classified information, the secretary's most used defense is that there were no emails with official headers that "marked" the email as classified. However, the FBI found 110 "unmarked" emails on her server that contained classified information at the time they were sent or received, and thousands more that were later categorized as classified. Again, if she was aware that her private server contained even a single sentence of classified information, she's indictable for knowingly and intentionally removing this information from State Department servers.
Ultimately, the secretary's claim of ignorance regarding classified information is not only implausible, but severely compromised by the many other falsehoods that she told (e.g., she turned over all her emails, she used one device, etc.) – the sheer volume of the secretary's untrue statements indicates that she's intentionally concealing, rather than being grossly ignorant.