It is possible, whether it fits your definition of easily is questionable, though.
Whole grain flour is made by grinding whole wheat/rye/... berries until you get a fine flour, a technique used since the neolithic age. The method that is still in use today is basically "rubbing the grains between a firm base stone and a moving upper stone", either shaped like a rolling pin or round and flat like a millstone. (Increase the scale and you get a classic mill.) So your mortar and pestle will work, even if they are not made of the types of sandstone, basalt or limestone that have the "right" mixture of coarseness and durability to make good millstones.
The drawback? Scale and time. You will probably need a lot of time, to get enough flour for a bread. For a starter, it should be ok, though.
If you think about buying a mill because you decide your super-fresh flour is worth the effort and cost, note that good manual mills with ceramic stones are almost as expensive as electric ones, but are way less comfortable. I make a lot of things myself and by hand in my kitchen, but I would draw the line at cranking a mill for half an hour just to get flour for one bread.
For a very "kitchen hack" style of grinding flour (but obviously not "stone ground"), consider your food processor (but check the manual first!): Pulse a cup or two of wheat berries untill you see "flour" and "grits" forming. Sieve off the finer parts, return the coarser to the food processor, add more grains and continue. You can even use the coarser parts for some kinds of wholegrain bread - a question of taste and recipe.