How do I use latexmk with MuPDF as the PDF previewer?

You have to specify $pdf_update_method = 2 in the configuration file, which tells latexmk to send a SIGHUP signal to the process when a change is detected:

$pdf_update_method = 2;
$pdf_previewer = 'mupdf';

1. Configure latexmk for your user in the file ~/.config/latexmk/latexmkrc (per the XDG specification) containing $pdf_previewer = "mupdf".
2. Specify the configuration's path:

latexmk -pdf -pvc -r ~/.config/latexmk/latexmkrc doc.tex

The default location for a user's configuration latexmk is either ~/.latexmkrc or ~/latexmkrc.