What I have done in the past and seen explained elsewhere is going to the services directories on the machine your GIS Server is installed on. That's provided you have access to that. Typically you will find the path to the original MXD there:
EXAMPLE
\<arcgisserver_install_dir>\directories\arcgissystem\arcgisinput\<service_folder>\<service_name>.MapServer\extracted\manifest.json
JSON would look something like this:
{"databases":[{
"byReference":true,
"onServerWorkspaceFactoryProgID":".,...",
"onServerConnectionString":"....",
"onServerName":"....",
"onPremisePath":"",
"datasets":[{"onServerName":" ...."}]
}],
"resources":[{"onPremisePath":"<<<<<<<path to .MXD file>>>>>>>",
"clientName":"....",
"serverPath":"<path to .msd file>"}
]}