If I download photos to icloud, can I delete them from my computer without deleting them from icloud?

If I download photos to icloud,

Which MacOS X version do you use?

How are you planning to store photos in iCloud? There are many ways to use iCloud with photos, but none will save space on your Mac:

• iCloud Drive: Any photo you store on iCloud Drive will also have a shadow copy on your Mac, so you cannot save space, see: iCloud Drive FAQ
• My Photo Stream: Photos you upload to My Photo Stream from your Mac, are also stored on your Mac. And My Photo Stream is only a temporary storage for a month. You cannot keep the photos permanently in My Photo Stream, see: iCloud: Photo Stream FAQ
• iCloud Photo Sharing: Shared Photo albums are also stored locally, and reduce the resolution of the photos: seeiCloud: iCloud Photo Sharing FAQ
• iCloud Photo Library (Beta): This is not yet available on a mac, but will be available, when the new Photos.app will be released. Right now you can use it from mobile iOS8 devices, iCloud Photo Library beta FAQ.Photos you store in iCloud from mobile devices can be accessed on your mac using the icloud web portal. You can however upload to iCloud Photo Library Beta from your mac using the Photos.app (Beta) on web interface at https://www.icloud.com

I am giving my computer to my son so I'm trying to get all my files off the computer first. I decided to export my photo library to an external hard drive rather than take any chances with icloud. Thanks for your help.

A copy on an external drive is the best solution.

If you export an iPhoto Library or Aperture library to an external drive, make sure that the drive is formatted MacOS Extended (Journaled) before you copy the photo library there. Otherwise you may have read errors or missing files, when you try to open the library again. See Format external drives to Mac OS Extended before using with Aperture

You can format external drives with Disk Utility, but you have to make a copy of all data before reformatting, because it will erase the drive.

Do you have a Time Machine backup of all files on your Mac? With a time Machine backup you can easily migrate all your documents and data to a new Mac.

You may want to have a look at this document:

What to do before selling or giving away your Mac - Apple Support http://support.apple.com/HT201065