Remove games from origin list
I'm not familiar with a way to actually remove the game from Origin, but there is a way to hide the game from actually appearing in Origin. Open the file
C:\ProgramData\Origin\InstalledGames.xml
The Battlefield Beta has an ID of 71171. Find that line and change
hidden="0" to hidden="1"
I'm not quite sure what the ID for the alpha is, but you could just follow a similar process to remove that one as well.
You need to contact EA support. They will disable whichever games you want.