This is a security feature which blocks local access while connected to the corporate network to protect it from your site and local Internet. If you feel this is not a risk you can enable split-tunneling allowing simultaneous access to both. This is done in different ways with different VPN clients. In most cases it has to be done by the VPN administrator. If you are using the Windows VPN you can do it your self. To do so on the client/connecting PC, go to:
network connections | properties of the VPN/Virtual adapter | Networking | TCP/IP -properties | Advanced | General | un-check "Use default gateway on remote network"