The projection looks like it matches this custom entry in http://spatialreference.org:
PROJCS["Stereographic_North_Pole",
GEOGCS["GCS_Coordinate System imported from GRIB file",
DATUM["D_unknown",
SPHEROID["Sphere",6371229,0]],
PRIMEM["Greenwich",0],
UNIT["Degree",0.017453292519943295]],
PROJECTION["Stereographic_North_Pole"],
PARAMETER["standard_parallel_1",60],
PARAMETER["central_meridian",249],
PARAMETER["false_easting",0],
PARAMETER["false_northing",0],
UNIT["Meter",1]]
http://spatialreference.org/ref/sr-org/8237/
Depending on the software you have at hand, that should be usable in one format or another.
If you want to transform a shapefile in lat-long to this grid system, then try this:
require(rgdal)
target = "+proj=stere +lat_0=90 +lat_ts=60 +lon_0=249 +k=1 +x_0=0 +y_0=0 +a=6371229 +b=6371229 +units=m +no_defs"
shgrid = spTransform(shlatlong, CRS(target))
plot the shgrid
object to make sure. You might get problems if the shapefile crosses the dateline or rounds the pole...
Not knowing how you've loaded your netCDF into R, I can't be sure how to crop it, but if its a raster then mask
from the raster
package probably does the trick.