We need to add -X to theirs.
Here's an example:
$ git checkout branchOne
$ git merge -X theirs branchTwo
This will merge everything in the desired way. But if some files were deleted from branchTwo that may cause some error.
In order to fix this just run git rm with the name of any files that were deleted:
$ git rm <DELETED-FILE-NAME>
Don't forget to perform git merge -X theirs after that. Of course, doing the actual removal with the git rm command will prevent the conflict from happening in the first place.
Note that a longer form option also exists. All you need to do is replace -X theirs with --strategy-option=theirs