If you clone a repository using --mirror, you will create a bare repository. That means:
"that Git simply contains version control information and working files (without a tree), and it does not contain a special .git subdirectory. Instead, it contains all the contents of the .git subdirectory directly in the main directory itself.".
The mirror option in clone is to make an βas isβ copy of your current repo, including notes and external links.
Being said, you are doing this on the wrong repo, you must use the original one to make changes, and the mirror will change accordingly.
Answering your question:
Is there a way to remove remote branches from mirror cloning, or do I need to build another clone for this?
I do not know what I know, except that the empty repository cannot be used as non-bare.
Maybe you need a plug, maybe if you explain a little better what you need. In any case, a year has passed since you asked the question.
Here are some related questions and doc:
Joako-stackoverflow
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