You need the -crop option, but this is not sufficient, as with image formats like PNG, the image may have a virtual canvas and you generally do not want such a virtual canvas in the output image. So, in doubt, you should use a +repage before the crop in order to remove virtual canvas offset information possibly present in the input image, and you should always do a +repage after the crop to remove such information (generated by crop, in particular), i.e. assume that the input may not be clean and ensure that the output is clean. This gives:
convert in.png +repage -crop <Width>x<Height>+OffsetX+OffsetY +repage out.png
And in your case:
convert in.png +repage -crop 640x620+0+0 +repage out.png
At the end of the -crop ImageMagick documentation:
It might be necessary to +repage the image prior to cropping the image to ensure the crop coordinate frame is relocated to the upper-left corner of the visible image. Similarly you may want to use +repage after cropping to remove the page offset that will be left behind. This is especially true when you are going to write to an image format such as PNG that supports an image offset.
If you use -crop while there is a virtual canvas, you may get an incorrect result, possibly with a warning like "geometry does not contain image".