This procedure is, to some degree, analgous to male circumcision since in both cases, no part of the sexual organ is cut off. In both cases also, it is only the foreskin, or outer fold of the skin, which is cut off. This is a form of mutilation. This procedure requires tying together the child's legs of nearly three weeks. Such necessity or need does not exist in female circumcision.
Nothing justifies genital mutilation.
In fact, no mutilation is allowed by Islam even in the battlefield. Not only are these two procedures unjustifiable, they are brutal, inhumane and in violation of Islam. The remaining question then relates to the first procedure. As such, there is no ground for a total ban on it. However, it is within the spirit of Shari'ah to restrict something that is permissible if discovered to be harmful.