import arcpy
arcpy.env.workspace = "path\to\workspace\MaintenanceDivisions"
arcpy.env.overwriteOutput=True
#variables
md = "MaintenanceDivisions.shp"
out = arcpy.CreateUniqueName( "clipped.shp" )
mfp = "dissolved.shp"
try:
    #clip polygons from selected area
    rows = arcpy.SearchCursor(md)
    row = rows.next()
    for row in rows:
        feat = row.Shape
        arcpy.Clip_analysis([mfpd], feat, out, "")
        row = rows.next()
except arcpy.ExecuteError as e:
    print(e)
del rows

import arcpy, os

outws = r'C:temp'
poly_single = r'C:temppoly_single.shp'  # The polygon to be clipped
poly_multi = r'C:temppoly_multi.shp'    # The clip features

rows = arcpy.SearchCursor(poly_multi)

count = 0     # Start a counter to name output polygons
for row in rows: # Loop through individual features of "poly_multi"
    out_poly = os.path.join(outws, "out_poly" + str(count))  # Assemble the output poly name and path
    arcpy.Clip_analysis(poly_single, row.Shape, out_poly)
    count = count + 1

# Clean up...Not necessary using "with" statement used in arcpy.da module
del row
del rows

import arcpy

p1 = "C:/p1.shp" #Multiple polygons
p2 = "C:/p2.shp" #Single polygon

with arcpy.da.SearchCursor(p1, ("FID", "SHAPE@")) as p1_cur:
    with arcpy.da.SearchCursor(p2, "SHAPE@") as p2_cur:
        for r2 in p2_cur:
            for r1 in p1_cur:
                intersect = r2[0].intersect(r1[1], 4)
                arcpy.CopyFeatures_management(intersect, "C:/{0}.shp".format(r1[0]))