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An attached stirge deals 5 (1d4+3) HP of damage at the start of its turn each round. The statblock states:

The stirge can detach itself by spending 5 feet of its movement. It does so after it drains 10 hit points of blood from the target or the target dies.

The monster description later states:

A stirge attacks by landing on a victim, finding a vulnerable spot, and plunging its proboscis into the flesh while using its pincer legs to latch on to the victim. Once the stirge has sated itself, it detaches and flies off to digest its meal.

Assuming rolling for damage rather than just applying average damage, should the damage be capped at exactly 10, at which point the stirge detaches? Or should the full damage from the damage roll that puts the total over 10 still apply?

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The blood loss damage is not capped at 10 (though in most cases it is functionally capped at 16)

The phrase "after it drains 10 hit points" can refer to a lot of situations. Here's an example of one

First round

  • Stirge rolls to hit, critical success. It does 2d4+3 damage. Rolls a 4 and a 4. 11 damage, but none of it due to blood loss.
  • Stirge has done 0 damage due to blood loss.
  • Is it "after it drains 10 hit points"? No, so it stays attached.

Second round

  • Stirge drinks blood. It does 1d4+3 damage. Rolls a 4 (man, lucky Stirge). Does 7 damage.
  • Stirge has done 7 damage due to blood loss.
  • Is it "after it drains 10 hit points"? No, so it stays attached.

Third round

  • Stirge drinks blood. It does 1d4+3 damage. Rolls a 1. Does 4 damage.
  • Stirge has done 11 damage due to blood loss.
  • Is it "after it drains 10 hit points"? Yes, so it detaches.

It will definitely detatch "after it drains 10 hit points": but until it has drained at least 10 hit points, it's not at that point yet. The time "after" it has drained 10 may include it draining more than 10, as in the example above.

The damage is "capped" in the sense that at most, it could start a turn having done 9 damage from "blood loss" and then do 4+3=7 more damage, effectively "capping" their blood loss damage at 16 (David Coffron pointed out that a stirge who is given a bonus to their damage roll somehow could even slightly exceed this limit: for example, if the stirge was a Beastmaster Ranger's companion). But they are otherwise not restricted by the rules as written.

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    \$\begingroup\$ There is at least one extreme case where you could deal more than 16 damage. Some features modify damage rolls directly and could increase the last blood drain to more than 10. A goblin druid wild shaped as a stirge, for example, could add their level to the damage via Fury of the Small \$\endgroup\$ – David Coffron Feb 22 at 19:25
  • \$\begingroup\$ OOoooh! Good point. I'll modify my answer slightly. \$\endgroup\$ – Gandalfmeansme Feb 22 at 19:27
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The stirge can do more than 10 damage

The attached stirge deals 5 (1d4+3) HP of damage at the start of its turn each round. When you roll for damage, that is the damage that is taken. Then, the condition for dropping is checked. If the HP drained is 10 or more, it then drops off.

Nothing about the dropping-off conditions indicates or implies that it caps damage, or will interrupt the damage-taking process. Once you roll the damage, that is the damage that the creature will take.

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The stirge deals all the damage, including any excess over 10.

The stirge detaches "after it drains 10 hit points of blood," but that triggering condition for detachment isn't met until after the full rolled damage number has been dealt as part of making its blood drain attack. In other words, the stirge won't detach until after it's already dealt a total of 10 damage, but the total could be in excess of 10 by the time it has a chance to detach.

So if, for example, the stirge has already dealt 7 blood drain damage so far and then rolls another 5, it would deal the 5, then detach, having dealt 12 total. The total is not capped to 10 because nothing in the feature says that it should be: the normal rules don't allow ticking down only 3 "unit points" of the 5 and discarding the other 2 in the middle of an attack without some special exception, and no exception is given for this feature.

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