Gender defenders accuse transpeople who change their genitals as "mutilating" themselves. Only a tiny fraction of transpeople undergo surgery so this is not an objection to transgenderism itself but only one form of gender expression. Even if this attack where true, it would not mean that all transpeople should repress their gender, just that they should refrain from that one gender expression. Still, that's not necessary.
Mutilation is defined by Webster as "to cut up or alter radically so as to make imperfect; to cut off or permanently destroy a limb or essential part." We can agree that male-to-female SRS and female-to-male chest surgery involves permanently cutting off body parts. Cutting your nails is also a permanent destruction of your body but no one objects to that. The difference is whether those body parts are essential and whether they make the body imperfect or actually improve the body but that is an extremely subjective question. No one argues about cutting nails, but many people believe circumcision is mutilation and have used this to attack Jews. The same charge has been brought against women cutting their hair. 1 Corinthians 11:14-15 has been been mistranslated "A woman's long hair is her glory" which implies that to cut it is to mutilate her.
An operative transexual holds the view that their pre-surgical genitals are not essential. If they felt they were taking away something essential, they would not have the surgery at all. In fact, some transexuals do value their birth genitals and decline surgery for that reason. But the opinion of operative transpeople is that they are not essential because they don't really belong to them. If you identify as a man, a vagina and vulva are not only non-essential, they are likely hurtful. After personal relationships, gender dysphoria caused by genitals causes the greatest pain in a transexual's life. Being able to resolve that heartache cannot possibly mutilation. There's nothing philosophical about this, simply the empathy for transpeople that God demands.
The idea that SRS is mutilation because it takes away standard lovemaking and reproduction is also flawed. I am asexual and a virgin but even I know that putting a penis inside a vagina is not central to sexual pleasure. Women tend to enjoy the foreplay prior to intercourse over intercourse and men tend to enjoy oral sex as much as or more than vaginal sex. Even Paul Cameron, who believes gay people will destroy the world, thinks anal sex is more pleasurable than vaginal sex. (Source) Besides, SRS does not stop sexual intercourse, it merely shifts it. Post-operative transexuals still have sex. The majority of transwomen are attracted to men and having SRS enables them to have penal-vaginal intercourse for the first time with their husbands. Similarly, most transmen marry women. Genitals do not define one's sex, but for gender defenders who believe it does, SRS changes their sexual relationship from lesbian or gay to heterosexual.
SRS also does not suddenly make reproduction stop. As I wrote in Objection: Trans People Cannot have Children, operative transexuals easily and often have children. The only thing SRS changes is that they will not have children in the "standard" method. But this never stopped Christians before. Do Christians object to cisgender, heterosexuals having en vitro fertilization or sperm donation because it is not standard or not natural? Plenty of transexuals will not have children after SRS and SRS may be a motivator, such as those with hysterectomies, making SRS a form of birth control. All birth control is unnatural by definition yet where are the Christians lobbying their government to ban condoms and the pill from married couples? Changing the menstrual cycle and performing vasectomies stop reproduction but are promoted as wise family planning, not mutilation.
Speaking of hypocrisy, gender defenders allow SRS on a regular basis, so long as the patient is intersex. They even demand it! SRS and hormone therapy among adults if fundamentally the same, whether one is female, male, or intersex. An intersex baby who undergoes genital surgery risks losing whatever fertility they had. Babies with a penis or large clitoris but are assigned female will lose much physical pleasure from their removed appendage. Yet gender defenders say the ends justify the means because it is more important that a person have a healthy gender than an untouched groin. While intersex and transgender advocates do not recommend cosmetic surgery on infants, we agree that being happy with our gender is easily worth surgery.
Of all things, Jesus hated hypocrisy most. Especially hypocrisy by the powerful "moral majority" to harm the powerless. We cannot have different morals for transpeople than cisgender people.
In short, whether mutilation is subjective and the issue is more concerned with stigmatizing transexuals not helping them. In the mind of transexuals, which is the only opinion relevant, SRS is never mutilation because the surgery always improves their body and their life.