This will affect the strength and longevity of your mortar. While I am not an expert here, there MUST be an optimal solution to such a problem. What mix will last as long as possible, hold strongly to the stone that surrounds it, be strong in compression, etc.?
Effectively, this is a multiple criterion optimization problem, that was long ago solved by practice to find the mix that best satisfies all the goals in combination. In fact though, if you go a wee bit in one direction, you will find that some of those goals will be better achieved, while the other goals will be harmed. This is how such a problem behaves. So the question now becomes, suppose I add some more sand (or other aggregate) to the mix? What will happen? Very likely (and again, I am just guessing at the exact effects right now as I talk off the cuff) the mix will become stronger in compression, but at some point it will erode more easily, get less sticky. Of course at some point, add too much sand and all you have is a pile of sand, which has none of the properties of mortar that you want.
Similarly, suppose I increase the proportion of cement? It makes sense that it sticks better to the surrounding stone now, but it is not as strong in compression.
Adding more water to the mix has other consequences, also optimized at the level you have been advised. So if you add water, the mix gets wetter, easier to work, stickier, but also sloppier. It won't stay in place. It may also change the cure time.
My point is that all of these parameters have been chosen to be optimal for the group of characteristics that define what mortar is and what it should do - the physical properties of the mortar. In fact, those parameters have been optimized by simple experiments by masons for years, until they established a mix that reasonably satisfies the best values at a point that is robust and stable to material variations.
Having said all of this, now I'll do a little actual research on the subject. For example, this site tells me that the ratio of sand and cement can be somewhere in the range of 1:2 up to 1:3, which changes the strength of the mix in terms of its ability to withstand compressive loads. It also mentions that adding gravel to the mix will increase the strength.
As I do more reading, I also see that the quality of the cement is a factor. With cheap stuff, you need more cement, so this probably is defined by the composition of the cement itself. (Is there lime in the mix? How much?)
I'll stop here, as there are MANY factors involved. What kind of sand do you use? Sand that is composed of perfectly round spheres, all of the same size, will be easily workable. But it won't be very strong. Sand that is "sharp" fractured with many sharp edges with varying particle size, will be less easy to mix, less easy to work, but stronger in terms of cured material properties.
A mix of aggregate sizes will change things too. Very fine sand will require more cement in the mix, as the tiny particles have more surface area for the given volume, so more cement is needed to coat the sand for good adhesion. But fine sand is easier to mix, easier to work, easier to stuff into a place. If the surface it must attach too is very irregular, it may stick better. But adding larger aggregate to a mix will increase the compressive strength, since large stone is stronger. (At some point, this turns the mortar into concrete.) Here is a quote that I find on one site:
"Mortar is a cement/sand/water (and usually lime) mixture designed for laying up masonry units like cement block, stone or brick. Mortar is "sticky" so it adheres to the block, stone or brick. Concrete is designed to stand alone."
While I am sure I have not covered all of the factors here, this should give you an idea. There are very many parameters involved. It is not only the amount of cement and sand that is important, but the exact cement formulation, the type of sand, the amount of water.