The IP which you pass as argument to tuxcut, is sent a packet telling him that its gateway's MAC address is your MAC address. Hence, that IP sends all the packets to you and if you don't forward it to the actual gateway, they're silently dropped.
E.g. If there are two PCs in a subnet, whose IP addresses are
IP_B and their MAC addresses are
Suppose that the PC with IP
IP_A tries to cut the net of PC with IP
As you know, every PC before sending a packet asks for the MAC address of the gateway if it is not available on its cache. So when the PC with IP
IP_B sends ARP Request for the MAC address of its gateway, it does that by MAC level broadcast: destination MAC is FF:FF:FF:FF:FF:FF.
IP_A PC replies to this with the ARP reply, which is unicast as sends its MAC (
MAC_A) as the MAC address of gateway. So
IP_B sends all packets to
IP_A which doesn't forward the packet to actual gateway.
P.S.: You can check this by using Wireshark while using Tuxcut.