How to cut image by top 30% in Unix?

You can crop a percentage of your image though in this case, to avoid running additional commands to get the image height and width (in order to calculate crop offset which by default is relative to top-left corner) you'll also have to crop relative to gravity (so that your crop offset position is relative to the bottom-left corner of the image):

convert -gravity SouthWest -crop 100x70%x+0+0 infile.jpg outfile.jpg

The command should be:

convert heart.png -gravity south -crop 100x70% +repage heart-out.png