Please see the attached graph. I would like to know if there's a convenient way in JMP to group the states together through the graph builder interface. For example, what if I wanted to group New York, Pennsylvania, and New Jersey into a single color called "Northeast"? Or what if I wanted to group the bottom 25 categories into an "Other" color?
I do not want to group things in the data table. I'd like to be able to draw this data from the data table and do the grouping inside graph builder.
Transform columns are one way to make data transforms that are local to Graph Builder (or any platform). Right-click on the column within Graph Builder and there are many built-in transforms.

The Formula... option will allow you to define more custom data transforms. One way to create the transform that you suggest will result in this script:
Graph Builder(
Size( 534, 456 ),
Show Control Panel( 0 ),
Variables(
X( :Year ),
Y( :Violent Rate ),
Overlay(
Transform Column(
"Custom Region",
Character,
Nominal,
Formula(
If(
:State == "New York" | :State == "Pennsylvania" | :State ==
"New Jersey",
"Northeast",
:State
)
)
)
)
),
Elements( Bar( X, Y, Legend( 13 ), Bar Style( "Stacked" ) ) )
);