My answer is more along the lines of "maybe." I don't think this is really about making the country safer. This is a Republican pandering bill. I do agree that if you do something heinous - assault, kidnapping, human trafficking, rape, murder, something that is inarguably violent and clear cut - then yes, by all means, you should be deported. People who commit violent crimes should not be permitted to stay. (And it should be noted that defending yourself or someone else does NOT constitute a violent crime. Republicans love stand your ground laws, so long as they only apply to white people.
And with the rise in xenophobic hate crimes and white supremacy, it's not at all unlikely someone might need to defend themself.) Misdemeanors are fuzzier. Even some felonies are fuzzy. If the crime committed is a non-violent misdemeanor offense, then no, they should not be deported. Sometimes people are driven to things like petty crime because of economic circumstances. And sometimes people just flat out screw up. We're all human. What we really need to do in those cases, with citizens and non-citizens alike, is to have a better understanding of the circumstances of these offenses. Very often, there are underlying reasons that need to be fixed. So in most cases, if they're non-violent offenders, I don't think they should be deported unless there are extenuating circumstances. But even that needs to be handled on a case by case basis. (If you do something like shoplift baby formula, that's very different from doing something like committing grand larceny, for instance. Even if both are non-violent.) And I don't think that any charge having to do with crossing the border should count in any way towards deportation. A lot of those are bogus and have been trumped up (pun entirely intended) in order to justify treating people like criminals when they aren't.