I am not 100% sure that it is the same, but when I use serve_site from blogdown it gives me a message with the line of code to run to kill the server (which is mostly doing to give you the exact instance number that has to be passed to the function) or it tells me to restart my R session (Ctrl + Shift + F10).. So if this command doesn't give you a message with the correct instance number to kill it than you can always just restart your R session.