Will I still have a geo-tag if I take a screenshot on my computer?
It sounds like you're talking about taking a screenshot on your Mac of the iPhone image, in which case, no, it won't have any geo-tagging information embedded.

However if you want to remove geo-tags from any photos (screenshots included) that you do have, the more convenient way is probably to use a tool like ImageOptim to strip out the EXIF data (which is the metadata containing geolocation data, amongst other things). That way you preserve the quality of the original, and you don't need to bother exactly trimming the size of the screenshot you take to the photo.