gdalwarp cutline without using a shapefile

It should be possible by using the -csql parameter http://www.gdal.org/gdalwarp.html and SQLite dialect http://www.gdal.org/ogr_sql_sqlite.html. Gdalwarp does not have an option for selecting the SQL dialect so you must help it by using some SpatiaLite database as a fake source for the cutline. GDAL selects automatically SQLite dialect when it reads SpatiaLite. The database must exist but it does not matter what it contains.

gdalwarp  -cutline foo.sqlite -csql "select ST_GeomFromText('POLYGON ((
0 0, 0 1, 1 1 , 1 0, 0 0))')" -dstalpha -of GTiff image.tif split_image.tif

BTW. your polygon was invalid because it was not closed. Using .csv file as source for cutline is straight forward as well.

Welcome to GIS StackExchange. Have you looked at the gdalwarp help page here http://www.gdal.org/gdalwarp.html? I think there's an example for GDAL > 2.2 combining different ways to cut/clip using extents and a csv file containing a WKT description.