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I know that I can add a selection to another and then subtract the overlapping parts. But if I have more complex selections, then it is very difficult to subtract overlapping selections. So my question is, if there is a other way to subtract overlapping selections in Gimp? Like the merge mode "Exclude intersection" in Adobe After Effects.

You can probably do it with channels. To essentially save a selection for future use, go to the Channels dock, click the "New Selection" icon, and set opacity to 100 and check "Initialize from selection." You can now go select something else in the image and when you want your original selection back, right-click the channel and select "Channel to Selection", restoring your original selection.
The use of this is that when you have your image and your two different selections stored as channels (they should be black-and-white areas), you can get the exclusion of the two selections, which seems to be what you are after.
Turn off your layers' visibility - it makes it easier.
One way or another, get the union of the two selected areas from the channels.
Then, turn on both channels' visibility so that it shows only the intersection.
Subtract this from the selection and then you have the exclusion of the selections!