I don't think the tree will mind what you use but it is much easier for you to use a pruning saw, especially if you are working in an awkward space. A small foldable pruning saw isn't really a very big investment and it is really useful particularly for branches too big for secateurs and to bendy for a bow saw. I use mine to prune fruit bushes and renovate shrubs as well as for trees.

it probably won't matter what kind of saw you use. Just avoid ragged cuts with gobs of peeled back bark, and of course cut just outside the branch collar (not sure how that would apply to a sucker since you are trying to kill it off). Also don't cut a horribly diseased tree and then a healthy one without sterilizing the saw.
And flora is right - a pruning saw is easier to get into hard to cut spots... I almost NEVER use my bow saw anymore.

i used a bow saw for decades.. though unwieldly.. they are tree saws ....

i would not recommend.. mostly cuz they dont work well ... lumber saws ... the teeth arent set properly.. to drag out the dust.. as you cut.. as in the type of saw a carpenter would use on 2 x 4 's .... or furniture ....

i thik.. the difference is that one is made for DRIED wood.. kiln dried.. and one for wet wood....

and that is the big difference ...

at the link is what replaced my bow saw ... two sets of surgically sharp teeth.. offset to pull out the dust.. and folds into my back pocket ....

see link .... though i found tractor supply knockoffs for $15 as late as 2 seasons ago ....

with this type of saw.. a man with decent hand/arm strength could take a 2 or 3 inch limb.. in 4 swipes .... lol... and a woman.. just a few more.. if she uses her authority ....

if you have a lot of pruning to do ... i suggest that the investment will pay off ... if you have the bows.. and just a little pruning.. so what.. use them .. and dont feel guilty.. nor worry about it ....

ken

Here is a link that might be useful: link

I carry one of those with me, always, when working outside. They can be stuck in a back pocket or a tool belt. They come with different blades, so if/when you buy one be sure to get the appropriate blade. Even the little cheapie ones work OK for a season. It goes with me not only for sucker removal, but when I cane out my bramble patches, and I have gotten disciplined enough to use one on those "wonder if this branch is too fat for my by-pass pruners" situations. They cost a lot less than a good set of pruners and that's how I ruin mine most generally. I took out a pretty hefty apple tree branch with a folding saw last week, as my pruning saw would not swing the angle I needed it to swing for lack of clearance. It's on of my fav tools, next to my drain spade and Japanese trowel.

Thanks for the replies! I thought the comparison between cutting green wood and dry wood was most interesting. I'm going to go back and take a good look at the quality of the cut the bow saw made, and if it's clean and crisp I'm just going to use it to recut the sucker stump that I left too long. If I think it looks ragged in any way I'll splurge on the pruning saw - but I only have three other young limbs I want to remove this fall/winter when the tree goes dormant, so my commitment to a new pruning saw is still iffy - lol. Of course by then I'll have the $$ to buy a good one, so I suppose I should add it to my tool shed...

You all gave me good things to consider to help me decide - thanks!