How do I stop devices from using the Internet using arp spoofing?

I have a virtual machine of Kali Linux and trying arp spoofing using the arpspoof tool I installed on Kali. I am trying to test out how I would stop devices from accessing the Internet. I have tried spoofing the router's MAC address by using arpspoof -i wlan0 -t (victim ip) (router ip). I run the "arp -a" command on my victims machine and it works as expected (the router's IP is associated with my Kali's MAC address and when I ping the router on the victim machine it doesn't get any replies from the router. HOWEVER, I can still use the internet. How is this possible? If I can't get any replies from the router shouldn't the internet not work?? (And yes... I am doing this on my own network)
http://dlvr.it/SjCKdY