Should negligence be a ground for criminal liability?

I can't say if it should be grounds, but it definitely can be. One can be jailed (at least theoretically) for speeding, for example, even where the cause of the offense was simply not paying attention to the speedometer or to the posted limit signs.

More serious crimes can result from more extreme negligence, usually referred to as recklessness or gross negligence. Various offenses involving vehicular homicide would be one type of case of this nature. A famous example is of someone shooting into a tent without knowing whether anyone was inside and without intending to harm anyone.