I wouldn't clear data for Google Play Services anyway, or not until I knew there was no other solution. There are a few things that will not work properly for a few days after you do that (which may or may not matter to you depending on what apps or services you actually use). There is nothing in your post to suggest that your problem is lack of space, so I would not worry about this.
To help I think I'll need to understand better what the problem is. So what do you mean by "the necessary WhatsApp", and which beta programme (the WhatsApp one)? You can't "empty" a beta programme: a beta programme is a scheme where people who are willing to test pre-release versions of an app ("beta versions") sign up to receive them. If the beta programme for an app is full all that means is that they are not taking on any more beta testers: it doesn't stop you using the regular (non-beta) version of the app. There is nothing else you can do.
So when you click on WhatsApp in the Play Store it takes you to the install page. This is what it should do. So what happens if you install it?
If you had heard of some feature of the beta version that you wanted to try, you just have to wait a little longer: if there are no problems with the beta then that will be released as the regular app shortly, so the only difference between being in the beta programme or not is that you will have to wait a little longer for a new feature.
