Maganer or maghaner means injure, damage or fatigue, and it's Quebec French, as has been mentioned, so it's good to have confirmation that the text comes from there.

"La définition de maganer dans le dictionnaire est traiter quelqu'un avec rudesse, brutalité. Tourmenter quelqu'un avec insistance, le tracasser. Fatiguer, affaiblir. Fatiguer, affaiblir en exigeant un travail, des efforts excessifs. Mettre quelque chose en mauvais état; lui causer du dommage, des dégâts. Marqué, fripé."

Here's the article Patrick mentioned, which I had also found:

"Il s’agit d’une forme dialectale du verbe, courant en ancien français, « mehaigner ». Ce verbe, d’origine germanique, qui signifie, « blesser », « mutiler », a donné des formes dialectales où le « h » aspiré (étranger au système phonologique roman) est concurrencé par l’occlusive vélaire [g]."
http://oreilletendue.com/2012/02/15/avec-ou-sans/

Applied to a voice, I think the usual adjectives that would be applied in English are raspy or rough. The idea is evidently a voice that sounds "damaged" or worn.

Raspiness is conventionally considered undesirable in a classical singer and associated with blues or rock singers, but I think it's the quality this is referring to. This is about the great soprano Renee Fleming who is now singing rock music:

"When the band kicks in and starts rocking, Fleming pushes a bit more at the edge of her voice, but you can almost hear her backing away from her technique, not soaring like she could but also not yet able to make her voice raspy or soulful or yearning in a rock way."
http://oreilletendue.com/2012/02/15/avec-ou-sans/

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Note added at 40 mins (2015-08-05 12:23:35 GMT)
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Sorry, wrong reference for the last quotation. It should be
http://www.popmatters.com/review/renee-fleming-dark-hope/

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Note added at 44 mins (2015-08-05 12:27:55 GMT)
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Really, in conventional terms, a classically trained voice that is "mag(h)anée" would be damaged or strained. In this text it's opposed to a pure timbre. The singer is saying that she'd like to sing with a less pure tone, a raspier tone. Raspiness is a quality more associated with male voices (you find references to tenors with a touch of this), and that fits also with the fact that singer would apparently like to sound more like "les gars".