Wow, you're actually going there. And no, it doesn't represent his penis, and I can't believe I'm going to actually write multiple paragraphs explaining Muatra to you.
Scratch that, I'm going to explain ALMSIVI Symbolism as a whole.
First of all,
Muatra is a literal spear that Vivec uses. So it's not his genitalia, thank you very much. However, being the Poet God that he is, there is a symbolic meaning behind it. So what is it?
Well, let's go back to ALMSIVI Religion and Lore. The Dunmer of Morrowind worship their three Living Gods, Vivec, Almalexia and Sotha Sil - But also three Daedra which are collectively referred to as "The Anticipations". Here's a quote from a book about it:
http://en.uesp.net/wiki/Lore:The_Anticipations
Boethiah is the Anticipation of Almalexia but male to her female. Boethiah was the ancestor who illuminated the elves ages ago before the Mythic Era. He told them the truth of Lorkhan's test, and defeated Auriel's champion, Trinimac. Boethiah ate Trinimac and voided him. The followers of Boethiah and Trinimac rubbed the soil of Trinimac upon themselves and changed their skins.
Mephala is the Anticipation of Vivec, but manifold and androgynous. Mephala taught the Chimer to evade their enemies or kill them with secret murder. Enemies were numerous in those days since the Chimer were a small [sic] with enemies on all sides. Mephala organized the clan systems that eventually became the Great Houses. Later, Mephala created the Morag Tong.
Azura is the Anticipation of Sotha Sil, but female to his male. Azura was the ancestor who taught the Chimer how to be different from the Altmer. Her teachings are sometimes attributed to Boethiah. In the stories, Azura is often encountered more as a communal progenitor of the race as a whole rather than as an individual ancestor. She is associated with Dusk and Dawn, and is sometimes called the Mother Soul. Azura's Star, also called the Twilight Star, appears briefly at dawn and dusk low on the horizon below the constellation of the Steed. Azura is associated with mystery and magic, fate and prophecy.
Each of the ALMSIVI is Anticipated by a Daedroth Lord which mirrors their persona and being. Note particularly the gender dynamics. Boethiah is male whilst Almalexia is female. Azura is female whilst Sotha Sil is male. Mephala can shift between genders whilst Vivec is both male and female at once.
This also reminds me of the Warrior / Mage / Thief Trinity which pervades so much of Elder Scrolls Lore and Symbolism. The Warrior being Masculine and thus Active, whilst The Mage is Feminine and thus Passive, with the Thief being the equilibrium-between. Now think of how in the ALMSIVI, Almalexia is The Warrior, being the most active and aggressive of the three, while Sotha Sil is The Mage, being the most passive and introspective of the three (Even being depicted as pregnant once), and Vivec is The Thief. He is the Warrior-Poet, after all.
Now, what does Mephala represent and how does it mirror Vivec? Well...
http://en.uesp.net/wiki/Lore:Vivec_and_Mephala
As known in the West, Mephala is the demon of murder, sex, and secrets. All of these themes contain subtle aspects and violent ones (assassination/genocide, courtship/orgy, tact/poetic truths); Mephala is understood paradoxically to contain and integrate these contradictory themes. And all these subtle undercurrents and contradictions are present in the Dunmer concepts of Vivec, even if they are not explicitly described and explained in Temple doctrine.
The Dunmer do not envision Lord Vivec as a creature of murder, sex, and secrets. Rather, they conceive of Lord Vivec as benevolent king, guardian warrior, poet-artist. But, at the same time, unconsciously, they accept the notion of darker, hidden currents beneath Vivec's benevolent aspects.
Mephala is the Daedric Prince of Sex and Murder, and thus paradoxically of Creation and Destruction (Sex being how life is generated, and Murder being a means through which life is ended). Note how this is paradoxical, but also very much aggressive. She's not the Daedric Prince of Procreation and Natural Death, after all.
Is Mephala's violent and paradoxical nature directly used in ALMSIVI Myth? Certainly:
http://en.uesp.net/wiki/Lore:The_36_Lessons_of_Vivec
And then the sixth spirit appeared, the Black Hands Mephala, who taught the Velothi at the beginning of days all the arts of sex and murder. Its burning heart melted the eyes of the netchiman's wife and took the egg from her belly with six cutting strokes. The egg-image, however, could see into what it had been before in ancient times, when the earth still cooled, and was not blinded.
It joined with the Daedroth and took its former secrets, leaving a few behind to keep the web of the world from disentangling. Then the Black Hands Mephala put the egg back into the netchiman's wife and blew on her with magic breath until the hole closed up. But the Daedroth did not give her back her eyes, saying:
'God hath three keys; of birth, of machines, and of the words between.'
In this Sermon, Mephala rips the egg-image of Vivec from his mother's belly with six cutting strokes, and upon seeing her "Burning Heart" (Heart as in a metaphor for something's center / soul) he merged with her and learned her secrets. Then Mephala put Vivec's egg back into his mother and revived her.
Mephala killed Vivec's mother, so that he could be properly born, the paradoxical relationship between Sex and Murder here exemplified.
So what is Muatra? Well, Vivec creates it in Sermon 14, after being forcibly married and abused by Molag Bal, Daedric Prince of **** and Domination, for 88 days. Muatra itself is an anagram for Trauma, which should tell you a lot. Vivec then uses Muatra to free himself from Molag Bal and slay their children (Which represent Vivec's own imperfection):
But Vivec made of his spear a more terrible thing, from a secret he had bitten off from the King of ****. And so he sent Molag Bal tumbling into the crack of the biters and swore forever that he would not deem the King beautiful ever again.
Vivec wept as he slew all those around him with his terrible new spear. He named it MUATRA, which is Milk Taker, and even the Chimeri mystics knew his fury. Anyone struck by Vivec at this time turned barren and withered into bone shapes. The path of bones became a sentence for the stars to read, and the heavens have never known children since. Vivec hunted down the biters one by one, and all their progeny, and he killed them all by means of the Nine Apertures, and the wise still hide theirs from Muatra.
Vivec here is creating a literal weapon out of his sexuality, both male and female (It is named Milk-Taker, not Milk-Giver, and those pierced with Muatra are withered of their vitality and become barren). In doing so Vivec is echoing Mephala, but in a different way: Muatra is Murder
through Sex. His sexual trauma weaponized in vengeance. The paradoxical relationship between Sex (Creation) and Murder (Destruction) wielded by a Hermaphrodite God.
This is what Muatra means. Stop thinking it's a dick joke.
