Imagine a Brick. A hard shell on the face contains a softer core. To cut a brick, you just scratch the surface a little, and then strike it and it cracks in a (roughly) neat line. If you placed wight on one side, and had a fulcrum, it would do the same.
Now imagine your wall, a bunch of bricks with mortar in between - and possibly several tons of pressure leaning on the wall. You decide to use an angle grinder to rake out the old mortar, and then fill in new mortar. You deeply scratch a few bricks. The wind blows, the house pushes down on the wall, and ... *CRACK* - the bricks "spall" (the face pops off) or crack, and the wall is now in worse shape than before.
Begin slowly, like this Instructable, and clear and rake (there are simple tools) by hand until you feel more comfortable with what you are doing.
Now. You might think the mortar is like a glue holding the bricks in place - but it isn't... well, before 1920 or so it wasn't. After 1920, it's all super-tough hydraulic cement that doesn't move and is watertight. Before? Your wall is like self-healing limestone... if tiny cracks appear, the mortar will actually seep Calcium minerals into the crack and become even stronger. That mortar can actually flex! Those minerals are transported by water. If your mortar isn't permeable (being lime based), then that water will go into the brick - which will damage the brick (again, *CRACK*). New house? totally different rules unless it was made with a lime mortar.
So the mortar is like a somewhat movable cushion for the bricks - it absorbs stress, it flexes, it wicks moisture around the bricks that do all the lifting. If you suddenly add a section of harder mortar? That stiffer section might crack out the softer sections nearby. Mortar less permeable than the brick? Water travels through the brick.
So, how do you know? Chemical tests can tell you the exact proportions and components of your mortar and brick. These might be expensive - but you'll be sure. A simpler test that gets you in the ballpark? Take a solid piece of mortar and drop it on a poured concrete floor. *TINK* - harder, more portland cement *THUD* - more lime.
You can actually compare small amounts of each type in the hardness spectrum to compare how they sound. But honestly, you're investing in this house - get the chemical analysis done.
Also, see http://www.oldlouisville.com/circa1900/brick-structures.htm
Learn the types of Mortar: http://www.cement.org/masonry/cc_mortar_types.asp
A great resource: http://www.nps.gov/hps/tps/briefs/brief02.htm
(Park service, who know a thing or two)
I'm using Type N, since I'm working in a load bearing part of the house. N is normally for above grade exterior, and is probably a little too hard/impermeable - but these walls don't have soil against them - so there is opportunity for them the breathe on both sides.