Hi Devon,
You could create a polygon object based on the MXD's data frame extent, and then use the object to clip the feature class. Here is an example:
import arcpy
from arcpy import env
from arcpy import mapping
env.workspace = r"C:\temp\python\test.gdb"
mxd = mapping.MapDocument(r"C:\temp\python\County.mxd")
df = mapping.ListDataFrames(mxd)[0]
xmin = df.extent.XMin
ymin = df.extent.YMin
xmax = df.extent.XMax
ymax = df.extent.YMax
pnt1 = arcpy.Point(xmin, ymin)
pnt2 = arcpy.Point(xmin, ymax)
pnt3 = arcpy.Point(xmax, ymax)
pnt4 = arcpy.Point(xmax, ymin)
array = arcpy.Array()
array.add(pnt1)
array.add(pnt2)
array.add(pnt3)
array.add(pnt4)
array.add(pnt1)
poly = arcpy.Polygon(array)
arcpy.Clip_analysis("Hospitals", poly, "Hospitals_clip")
del mxd
Hey Jake, just wondering what the reasoning is behind everything broken up like that? This is a similar code I use, I don't remember if I wrote it or stole it from someone. If I did steal it credit to them.
import arcpy
mxd = arcpy.mapping.MapDocument("CURRENT")
df = arcpy.mapping.ListDataFrames(mxd,"Layers")[0]
extent = df.extent
array = arcpy.Array()
array.add(extent.lowerLeft)
array.add(extent.lowerRight)
array.add(extent.upperRight)
array.add(extent.upperLeft)
array.add(extent.lowerLeft)
polygon = arcpy.Polygon(array)
...