If the wall is the original dirt/hill/yard retainer and it was designed as such with a stone face for nicer looks, then the strength of that "mortar" may be one of several different versions.
From mr. Google -
There are several types of mortar, including Type M, S, N, and O, each with different strengths and applications.
When I rebuilt my 2-flue chimney, I opted for Type M, knowing I was going up 30 plus feet and thought I wanted it as strong as possible.
That choice has yet to be tested - maybe one of my grandkids will be cursing my name on the next rebuild!
I have also seen where folks build a stone wall with wooden casing surround, carefully placing stones in the form and them pouring regular concrete around the rocks, moving them just enough to embed them fully.
A hard bristle scrub brush is then used on day 2 to make the face of it pretty.
My point is - your old wall could be constructed in so many ways - you'll either need to do some real digging to ascertain it's original style, or just make it solid to repel any further intruders!
Good Luck, and if possible, give us a follow up on the completed project!