What you seem to be misunderstanding is the layout of Helm's Deep. The Hornburg, defended the actual "Helm's Deep" The space we can see middle of the picture between the two rocks.
At Helm’s Gate, before the mouth of the Deep, there was a heel of rock thrust outward by the northern cliff. There upon its spur stood high walls of ancient stone,and within them was a lofty tower.
The wall was what stood between that armies and Helm's deep, as the Hornburg was inpenetrable. Once the wall falls, the Hornburg becomes completely surrounded and the attackers now have full strength to enter the Deep (the cleft between the rock, behind the Hornburg). Saruman is identifying that once the wall is destroyed they have access to the deep. This doesn't mean the Hornburg is lost, but at this point, Theoden is surrounded entirely.
There are no "side doors" to the Hornburg, not in the films or in the books. Hence why Theoden was able to ride out and none of the orcs had already breached the fortress. (Excluding the side gate that Aragorn and Gimli jump out of, but the orcs didn't have access to that and didn't know it was there.
Tolkien's drawings of Helm's Deep and the Hornburg