However, it's also possible to have access (in the same time) to Internet.
To do this on ASA, you have to configure some NAT rule.
All traffic that will go to Internet have to use the Internet facing interface like source IP address.
The configuration below is an example that can be applied:
ip local pool Pool_VPN 192.168.40.10-192.168.40.250 mask 255.255.255.0
!
interface GigabitEthernet0/1
description Outside Facing Interface
nameif INTERNET
security-level 0
ip address 199.199.199.199 255.255.255.240
!
object network NAT-VPN-POOL
subnet 192.168.40.0 255.255.255.0
description Pool VPN
!
object network NAT-VPN-POOL
nat (any,INTERNET) dynamic interface
All traffic with VPN IP Pool source address and with Internet destination will match this NAT rule.
Source address will be modified with the outside interface.