Mark the German text as German instead of English. You can set the language for text on the Font tab of the paragraph style or character format window. If you have a dictionary for German, Libre will spellcheck the German as well.

On the paragraph style window, the tab is somewhat to the right. Note: it's important that you spend some time to get comfortable with those windows and their tabs, so that you know where to find some formatting features when you need them.
If this doesn't fix your problem, you should reset your user profile. See https://forum.openoffice.org/en/forum... .
Have you tried turning off Automatic Spell Checking? (Menu Tools) By the way, the red wavy lines are only there for editing and will not appear when you print a copy of your document.
Wouldn't that also turn off the English spell check?
Yes it would. If you want to retain the spell checking feature, the more complete answer provided by @floris v should be the preferred solution.