No, only one curse per item from Blood Artisan
There’s a few ways to interpret this, but none of them seem to me like they should result in multiple curses
Strict RAW—Blood Artisan doesn’t apply to upgrades
When you make magic arms and armor or wondrous items,
If you are improving a magic item, you aren’t making it. “Making” only applies to the original creation. That means you don’t get a 75% discount, but also have no concern about curses, when upgrading magic items.
This is a really pedantic reading, though, as it’s just unrealistic to hold Wizards of the Coast to that standard. They weren’t that careful with their wording, and when adding new magical features to an item, “the cost to do so is the same as if the item was not magical.” That is, a +2 longsword is supposed to always cost the same whether you did it all in one go, or created a +1 longsword and then upgraded it to a +2. This reading would break that.
Ignoring that—the item is cursed
If we are ignoring the specific thing written about when Blood Artisan applies—and I’d argue we should—the wording of the sentence about the curses also does not support adding multiple curses:
the item is always cursed
That is, the statement here applies at the level of the item, not at the level of the particular effects or particular effort to add them. If the item is already cursed, the statement “the item is always cursed” is already true, and nothing happens to make it true. If the item isn’t already cursed—but only then—the item becomes cursed when the blood artisan adds something to it.
This is still relying on pretty specific wording from Wizards of the Coast, though—it’s not clear that relying on “item” here was any more wise than relying on “make” in the previous sentence. The reason we ignored “make” before is because we were kind of assuming that they didn’t actually think about upgrades at all, because they often forgot about that case. But then that would apply just as well to this sentence.
Going beyond RAW—the crafting history shouldn’t matter
Again, the rules go out of their way to make it not matter if something was crafted all at once, or crafted in stages. That should still apply here: a +2 longsword crafted with Blood Artisan should not have twice as many curses if the blood artisan crafted it as a +1 longsword originally and later upgraded it to +2. That kind of thing is something the rules don’t want us to keep track of. And this is the real reason we shouldn’t take “make” too seriously, but should accept “item” as the appropriate level at which the curse is applied.