The only problem with The New Republic's story is that it doesn't live up to its headline. "NYC Police Said Stop-and-Frisks Reduce Violent Crime," it is titled. "This Chart Says Otherwise." Then it shows this chart -- which doesn't offer any data on actual crime rates.
So this chart actually shows that the number of stop-and-frisks isn't related to the crime rate.
Since the numbers of crimes are (happily!) low, we can also look at it as a rate-of-change. If crime was tied tightly to the number of stop-and-frisks, we'd expect to see the red bars (crimes) drop as the blue bars (stops-and-frisks) rise, and vice versa. We don't.
But the most robust illustration is what has happened over the course of 2014, versus 2013, as stop-and-frisks have all but vanished under Mayor Bill De Blasio (D) (who took office in January). In every major crime category, crime rates have fallen.
There's value to this assessment outside of the utility of stop-and-frisk (which, we will note, isn't disproven by the lack of a correlation here, just severely undermined). For example, former mayor Rudy Giuliani (R) has made a new career getting on TV to talk about how he knows all about crime and its causes since he oversaw a steep decline in the city's crime rate -- using things like stop-and-frisk. But it's also very clear that Giuliani benefited from the fact that New York City crime rates were already falling before he took office, as they were nationally.
In fact, there are competing theories as to why crime rates fell. Based on the data at hand, however, it's safe to say that the role of stop-and-frisk in that dip is far from proven.