If you pray Tarawih followed by Witr in the mosque, can you pray Tahajjud later at night since Witr is already done?

No issue with this, the key point being the Prophet ﷺ said لا وطران في ليلة that there's no two Witr prayers in one night meaning you don't repeat the Witr prayer. So the Sunnah would be to pray with the imam, finish with the imam. If you're going to pray Tahajjud later on what you would do is when the imam says As-salamu alaykum wa rahmatullah, As-salamu alaykum wa rahmatullah for Witr, you stand up and you pray an extra rakah. Your intention is not the intention of Witr. Your intention is that it's an extra Nafl prayer. And then you pray your Tahajjud and after your Tahajjud you pray your Witr. That's the better way to do it. However, if you were to finish with the imam and say As-salamu alaykum wa rahmatullah, As-salamu alaykum wa rahmatullah when he finishes his Witr and then later on pray Tahajjud, again no issue but just remember you do not pray an extra Witr.