For reasons unknown the Skype for Mac developers want it to run as a fully-fledged app, including having a Dock icon at all times. Most messenger/talk apps let you run them as a simple menu bar icon, freeing up the Dock from clutter.
To get rid of the Dock icon for Skype you’ll need to use a quick hack. There’s a handful of guides on the Internet, and even a handful of apps that used to do the job, but pretty much everything you’ll find is out of date. Below is a guide that works on the current 7 release for Mac, and was written in September 2016.
Start by closing Skype, and then opening the Terminal app, which you’ll find in the Utilities folder of the Applications list of Finder.
Copy and paste-in the following, which is a single line – triple-click it to highlight it, then copy it via Cmd+C:
defaults write /Applications/Skype.app/Contents/Info LSUIElement 1
Nothing will appear to happen, but you can now close Terminal. Run Skype and there won’t be a Dock icon from now on (if you’ve added the Skype icon to the Dock you can drag it off to remove it).
You can close the main Skype window and all you’ll be left with is the Skype menu icon to set your status. To open the main Skype window in future, just double-click the Skype icon in the Applications list or just open it via Spotlight – tap Cmd+Space, then type Skype, and hit Enter.
If you’re away from your Mac, or just don’t have the main Skype window open as described above, new text messages or missed calls appear as notifications. To make these stick around rather than disappear when you’re away from your Mac, open System Preferences, click the Notifications icon, select Skype in the list, and select Alerts on the right. If you get several messages or calls the notifications will stack on top of each other.
To restore the Dock icon, just drag Skype to the Trash, and then reinstall it from Skype.com.