First of all while Linux Mint is base on Ubuntu nonetheless it is not an officially supported Host/Guest so it's not unreasonable to expect some issues, especially with VMware Tools. That said, while I do have a Linux Mint VM I am not where I can access it however in an Ubuntu VM I have no problem using the following two commands to bring eth0 down/up.
sudo ifconfig eth0 down
sudo ifconfig eth0 up
These command clealy change the state of eth0 without error and I'd expect it to also work in Linux Mint however cannot confirm that at the moment. I'd act just as if this was a Physical Machine and do the expected diagnostic/troubleshooting to see where the issue lies.
