var studs = db.students.find();

for (var i = studs.length()-1; i >= 0; i--) {
    db.students.update( 
        { _id: i }, 
        { 
            $pull: { 
                "scores": getMinScore(studs[i]) 
            } 
        } 
    );
}

function getMinScore(stud) {
    var i, minScore = stud.scores[0].score;
    for (i = 1; i < stud.scores.length; i++) {
        if (stud.scores[i].score < minScore) {
            minScore = stud.scores[i];
        }
    }
    return minScore;
}