UNC path cannot be a current working directory (that's a Windows limitation, it has nothing to do with SQL server).
As @lit already commented, you can temporarily allocate a drive letter for a UNC path and change working directory to it at once, using pushd
command.
Alternatively, modify your WinSCP script not to rely on the current working directory.
Just use full UNC paths in the script, like:
get "/remote/path/*" "\\fileServer\RemoteMirror\"
See also Using batch file and WinSCP to download files from the FTP server to file server (shared folder)
Or, if you need to make the script working with different directories, use a parameterized script:
get "/remote/path/*" "%1%\"
And run it like:
winscp.com /ini=nul /script=Remote_Mirror_WinSCP.txt /parameter \\fileServer\RemoteMirror
See a full example for using parameterized scripts.