Yes, but it takes a careful hand and the right tools. A mason removes old mortar with a grinder blade matched to the joint width, or by hand with a chisel on tighter joints, keeping the blade centered so it never touches the brick itself. A grinder that wanders even slightly chips the arris, the sharp edge of the brick, and that kind of damage can't be undone once it happens.
The main tool for cutting out old mortar joints is a grinder fitted with a blade sized to match the joint, wide enough to clear the old mortar but narrow enough to stay off the brick faces on either side. Corners and tight spots where a grinder can't fit safely get finished by hand with a chisel. The combination of the right blade width and a controlled, unhurried pass is what keeps the brick edges intact.
Older, handmade or soft brick is even less forgiving than modern machine-made brick, since it chips more easily under pressure. On those walls, more of the joint typically gets cut by hand rather than power tools, which takes longer but protects brick that often can't be replaced with an exact match if it gets damaged.
Chelo's crews are trained to match the grinder blade to the joint and control depth so the fresh mortar has enough of a groove to bond into without over-cutting into the brick. It's a slower process than just grinding straight through, but it's what keeps a repointing job from turning into a brick replacement job.
This is also where DIY repointing attempts tend to go wrong. A homeowner working without the right blade width, or rushing a pass to save time, is far more likely to nick brick edges than an experienced mason working slowly and checking depth as they go. Once the arris is chipped, there's no undoing it short of replacing that brick, which is a much bigger job than the repointing was ever meant to be.
More on this from Chelo's Brick & Stone.
Chelo's Brick & Stone serves Hillsville, Galax, Wytheville, Fancy Gap, and Independence, VA. Call for a straight answer and a free on-site estimate.