Here's how I handled selecting multiple polygons scattered throughout an area that clips from a single raster image(DEM). My area covered four counties, so I had to change the DEM (hardcoded) each time I ran it. May be a little klunky, but it works. All of my polygons begin with the same naming convention. I use a lot of print statements in my code to verify it's running and that I'm getting the expected outputs. My sanity check....
import arcpy, os
from arcpy import env
from arcpy.sa import *
arcpy.CheckOutExtension("Spatial")
env.workspace = "//w63-atlas/Stormwater/Waterways/Structure Flood Severity"
bslash = "\\"
Raster = bslash+"\\w63-atlas\Stormwater\AMEC\Platte\TOPO\DEM\platte_dem"
print " Raster lowkayshunn ",Raster
tile = raw_input("Enter FEMA TILE : C4, C5, C6, D4, D5, D6, E5, E6, F5, F6, G5, or G6: ")
outFC = "//w63-atlas/Stormwater/Waterways/Structure Flood Severity"
prefix = "Export_"
suffix = "_Culv*_1.shp"
depiwant = prefix+tile+suffix
slash = "//"
aewout = outFC+"/"
print "aewout = ", aewout
print "depiwant = ", depiwant
outFC = outFC+"/"+depiwant
print "Raster = ",Raster
print "outFC = ",outFC
arcpy.env.scratchWorkspace = "//w63-
atlas/Stormwater/Waterways/Rasterdatasets.gdb"
gdb = "//w63-atlas/Stormwater/Waterways/Rasterdatasets.gdb"
print "gdb = ", gdb
fcList = arcpy.ListFeatureClasses("Export_"+tile+"_Culv*_1.shp")
print "Shape files to clip from: " , fcList
arcpy.AddMessage(Raster)
for i in fcList:
print "aewout+i ",aewout+i
print "Shape file: ",i
Culvnum = i[14:-4] #strip out the name
rasnew = gdb+"/"+tile+"rz"+Culvnum[:-2]
print "Culvnum ", Culvnum
outExtractByMask = ExtractByMask(Raster,i) #create temp raster file
arcpy.AddMessage(outExtractByMask)
print "Raster image = ",Raster
print "current Culv = ", i
print "outExtractByMask = ", outExtractByMask
outExtractByMask.save(rasnew) # save temp raster to final name
print "Raster CLip NAMe: ", rasnew
print "All done creating raster files. NEXT !!!"
exit