I have used a sawzall before, with marginal results. It can beat you up in a hurry if the blade snags.
Most of the time I use a chisel or 4" grinder. You have to be real careful with the grinder or you will nick up a lot of brick.
If the existing mortar is solid and sound then don't take a lot of it out, leave well enough alone. Where it is already eroded you don't have to take a lot more out. If it is coming out easily, then tapping away with a chisel is the way to go.
Finally got to fill some joints today! There was a learning curve... but think I'm starting to get the hang of it. I mixed small quantities and took my time. The vertical joints are definately the most challenging. One thing I am wondering about though- is the white residue left on the bricks... I'm probably making a bit of a mess, but surely there must be a way to get off the white junk? Will it just wear off?
All in all I think it's looking better... Obviously not a pro job... but better than doing nothing. The mortar is much brighter than I had thought it would be... I added some dye on my last mix and that ended up looking much nicer (upper left). Now I just need to get some taller equipment to stand on!