No, each instance of Death's Gauntlet would require a separate standard action to end.
While this requires interpretation of the rules, it's not really a stretch.
Stacked ongoing damage requires separate saves
From page 173 you mention:
For example, if the Efreet with the flaming sword has hit you twice with an attack that deals 10 ongoing fire damage, you’ll take 20 fire damage at the end of your turn, and then roll a save against each of those ongoing damage effects (two total).
It would follow that if you have save twice from two effects, you'd have to apply any alternative methods of ending those effects twice, too. But if that's not enough to convince you, lets take a closer look at the spell.
Math of Death's Gauntlet
We'll compare it with Chant of Endings, another necromancer at-will damage spell that is much more straightforward. Chant can only target the enemy with the fewest hit points, but that's not a very severe limitation. At the first level, given Int of +4, it'll do 1d10+4 or 9.5 damage. Death's Gauntlet would do 1d4+4 ongoing, or 6.5+6.5/2+6.5/4+..., which roughly equals 11.5. A difference of 17%.
At 5th level, assuming our necromancer has acquired a +2 implement and Int of 5, Chant will deal 6d6 + 2 + 5*2 = 33 damage (ability mods get doubled in the Champion tier). Death's Gauntlet will become 4d6 + 2 + 5*2 ongoing, or 26 + 26/2 + 26/4 + ..., about 45.5 damage. A difference of 27%.
By Epic tier, the difference in damage is only 1d10, but Chant of Endings can target two creatures if invested with feats, while Death's Gauntlet can target MD. It gets slightly too complex for this simple analysis.
While Death's Gauntlet scales better, it's important to remember that not only is it very swingy, it's also possible to lose extra ticks of damage due to the target having the audacity to die. The spell is also not going to prevent a creature from having at least one more turn. Overall, both spells seem to be on par, with different tactical uses.
Death's Gauntlet in play
The provision for ending ongoing damage strikes me as mostly a flavor thing, at least to start with. There's some great roleplaying opportunities to be had here that simply dealing damage wouldn't afford.
It can become necessary for the creature to burn its action to get rid of the skeletal limbs if it's particularly low on hit points. Once you're in the Champion tier, though, and take the feat that makes the save from Death's Gauntlet hard, it gets much nastier. Now it's more of a lockdown spell. It's not a hard lock, but it presents the target with an unappealing choice: waste a standard action, or keep taking damage with little chance of saving.
None of which suggests that Death's Gauntlet is somehow overpowered when multiple instances of the spell are applied to the same target, which would have warranted letting the target remove all of them with a single action.