There is currently no way to do this with the UI, but an enhancement request for this feature can be found here: Allow to unset the current iteration (79007). Also, here are a few work arounds you can try. 

I believe this would be the best solution based on what you described: 
1) Create a new iteration (call it something like current iteration placeholder)
2) Place the new iteration at the bottom of the timeline
3) Assign the new iteration as the current iteration
4) Save
5) Archive the new iteration
6) Save
This will mark that iteration as completed.

Another possible solution:
1) Move the current iteration to another timeline
2) Move the iteration back to its original place.
3) Save
This will get rid of the current iteration entirely.

If you don't have another timeline, you could:
1) Create a timeline
2) Move the current iteration to that timeline
3) Move the iteration back
4) Delete the timeline
5) Save
 This will not create a new timeline and the current iteration will be removed entirely.