Assign different taxonomy terms to translations of content
If you don't want the node translations to share the terms they are tagged with you need to make the Taxonomy term reference field translatable. Then you will be able to enter different values into that field depending on which language you're editing. 

You can enable the translations for Fields under Configuration &gt; Regional and language &gt; Content language and translation (/admin/config/regional/content-language). 

Tick the box for your Taxonomy field and hit the "Save configuration" button at the bottom of the page. 

After that you'll be able to save the translations with different values for that field than the original. The translations in languages other than the default one will probably have that field empty before you edit them, they will not "inherit" the values from the default translation out-of-box.