Add nonat config for the DMZ interface. For example, assume this configuration:
ip address inside 10.1.1.1 255.255.255.0
ip address dmz 172.16.1.1 255.255.255.0
ip local pool vpn_pool 192.168.1.1-192.168.1.254
access-list split_tunnel permit ip 10.1.1.0 255.255.255.0 192.168.1.0 255.255.255.0
nat (inside) 0 access-list split_tunnel
Enter these commands:
access-list split_tunnel permit ip 172.16.1.0 255.255.255.0 192.168.1.0 255.255.255.0
nat (dmz) 0 access-list split_tunnel