Since GDAL 2.1 GDAL and OGR utilities can be used as library functions, so this task is incredibly simple now:
from osgeo import gdal
ds = gdal.Open('original.tif')
ds = gdal.Translate('new.tif', ds, projWin = [-75.3, 5.5, -73.5, 3.7])
ds = None
Is there a similar library in Java to replace gdal_translate.exe call?