Late to the party, I just saw this and I'd say it's not ambiguous that way in Swedish, we usually say ett hårstrå for one hair, literally 'a hair straw'. Using ett hår for just a single hair is rare (outside of set expressions and translationese). I would also use another verb for cutting that: Hon klipper av hårstrået.
Jag läste the instructions för denna section och det förklarde att på svenska, man säger "I am brushing the teeth" instead of "my teeth," och så vidare. If the possible translation had been "She cuts her hair," I would have chosen it. Please change the translation words because "She cuts the hair" is a poor translation.
One thing I don't really like about duolingo is that it puts THE hair instead of hair.. it makes the sentence very ambiguous, so I always get confused.. it uses THE (object) instead of (object) in places where it needs to be specified (or not).. I don't know.. is it just me? It's really frustrating sometimes when I get it wrong because of this...
Speaking with my professional language-teaching hat on: It is not English to say ‘She is cutting the hair.’ She cuts hair (general) or She is cutting (the woman’s) hair (specific example). The translation as given currently is incorrect - perfect Swenglish but bad English and really should have been changed by now.
We do accept nine different variations, for that reason. It's just that the default translation is automatically chosen for the reverse "translate into Swedish" exercise. So if we want to teach this idiomatic translation in Swedish, we have to use unidiomatic English.