I don't understand why you want to completely remove your LAN connection but:
If you go to your device manager, and right-click on the Network Adapter that you want to remove, you should have an un-install option. Click it. Once it removes it, shut down the computer and open the case. Remove the network card from the machine. That is the only other way than disabling it as Jonny has suggested.
If the network card is an onboard NIC, you should be able to completely disable it from the BIOS. Depending on the BIOS manufacturer, you will use whatever key that is used at bootup to enter the BIOS options (normally these keys are either: F1, F2, F12, or del for most manufacturers) In there you should find something referring to an onboard network interface, card, NIC, etc. You should have a disable option there.
Hope this helps.