How do I download photos from iCloud Photos directly to my External HD? I have no more storage on my mac.

If you are using an internet browser to download photos as described in the "Download copies of your photos and videos from iCloud.com" section of Archive or make copies of the information you store in iCloud - Apple Support set the Download folder of the browser to your external drive before you start.

How you do that varies by browser. If you are using Safari, go to Safari Preferences > General (at the top of the Preferences window) > File download location.

Note that if your Photos Library is on your Mac drive, you can move it to an external drive as described in Move your Photos library to save space on your Mac - Apple Support

If you have iCloud Photos turned on in the Mac and you move the Photos Library from your Mac you may not need or want to do what you were planning to do.

See this thread Cloud and Hard Drive - Apple Community

Photos can’t be transferred directly from iCloud to an external hard drive for that you need to set up iCloud photo library see the article Set up and use iCloud Photos - Apple 

And its preferences Change preferences in Photos on Mac - Apple  open finder > Go > home > your user name > pictures either drag and drop Photos Library.photoslibrary to an external hard drive , the second method is right click on Photos Library.photoslibrary and click on show package contents in the upcoming column , you can also drag and drop complete masters folder to an external hard drive that is connected .

Also as per the article Back up the library in Photos on Mac - Apple 

Manually copy your library to an external storage device: Drag the Photos library (by default in the Pictures folder on your Mac) to your storage device to create a copy.See this article also

Photos library - Move your Library to an external storage device