Is there a way to select a group of vertices and perform a bisect/cut along them? For instance if I drew a car's body, but want to then cut out the door so that it can open, what do I need to do to accomplish that? Should I just select all the vertices and hit "P" to make them their own object or something?
There is a Bisect Operator that might do what you want it to.
3D View > Mesh > Bisect, requires a Face Selection
This allows you to split the mesh along a plane you can define by dragging, or numerically. If your Operator Panel is not open, hit F6 to show it. It come with a bunch of useful options, like
Fill, which fills the cut edges with faces Clear Inner/Outer which remove one or both sides of the cut Axis Threshold that gives the cut adge some fuzzines in where the cut-off happens.
If your vertices are already defining you cutting edge, it would be more efficient to simply separate the part into its own mesh by selecting it and hitting P to do Separate > Selection