You are on the right track, but need a different tool. A VPN allows a remote computer, one that is on a different network, establish a virtual tunnel to your local network. In doing so, you create a virtual network adapter on the remote host and it gets assigned a local IP address. Routing to and from the local network is then performed via this virtual adapter. For this reason, VPN only works with remote locations, though, you can still establish a VPN connection when you are local, it just doesn't do much.
There are two, perhaps three, methods that I know of to accomplish what you are after. The first two are to either use Samba or NFS. Samba emulates Windows' networking functions and allows Windows based computers to share files with your Linux system. To configure basic sharing is pretty simple and straight forward, yet it also supports exceedingly complex and secure networks too. NFS is a native Linux approach for file sharing. I haven't read up on it much and can't provide a lot of information on it, sorry.
I mentioned a possibly 3rd approach. Depending on the capabilities of Mint, you may be able to simply select the properties of the directory or file you wish to share and set it as shared. This may use NFS in the background. I suggest this because it is exceedingly simple and is worth trying first.
In any of the above approaches, you will need and want to consider any security implications. In sharing your folders over a network, you will be opening ports to service. Unless you want this ports to be accessible to the world, you will need to ensure that your upstream router blocks them or configure your firewall to only allow connections from your local hosts.