The first time we are introduced to Guts' sword, the Dragonslayer, in Berserk is in the opening seconds as the master blacksmith Godo mends it. The first time we are properly introduced to it however is when Guts cleaves a brigand clean in two, taking out a solid wooden table and most of the floor with him. It's a monumentally absurd weapon, as tall if not more so than the wielder and likely just as heavy, outside of fiction it would be impossible for any human to wield.
For the 1997 anime at least, this introduction is misleading as the sword that we see for the remainder of the series is just as tall but not quite as absurd. It's not the only one of course - Guts grows up and events transpire which changes who he is and subsequently what he wields.
The first sword we see Guts with is the one he takes from his abusive adopted father Gambino and is the one used to slay both him and the wolves which hound Guts' flight from what was once his home. It is a larger version of this sword we also see a teenage, mercenary Guts defeat the rotund Bazuso with. As Guts' grows up, his sword is shown markedly fatter but still just as long.
It isn't until after his fight against a hundred men that this sword is damaged and eventually shatters when facing Boscone in the assault on Doldrey - this is then replaced by Zodd's massive blade which Guts' uses to carve through both the general and his horse in one swipe. This is reforged into a pointier version of the now iconic shape and is shown breaking through solid oak doors as easily as it does human foes.
The most telling element of Guts' relationship with his sword is not when he has it on him (sleeping, wounded, in a water fight with Griffith) but when he doesn't. The first time it is absent from him there is a fleeting thought but he is seen wielding a dagger without a another thought. The second time it is absent is during the Eclipse when, after chasing a gaunt and helpless Griffith, Guts is caught in that hellish world without it. Here though there is no lament, just singled minded resolve as he carves through demonic minions with anything at hand - a dagger, horns and fists if need be.
The adoption of the Dragonslayer - originally forged for the once king of Midland - is at once pragmatic, but also a statement of purpose. Guts' sword always reflects the measure of the challenge he faces, whether that's the gusto of an overzealous mercenary, a hundred men or the full force of destiny, Guts' says himself that he is only happy when swinging his sword and watching sparks coruscate from the blade.
Indeed his reason for originally leaving the Band of the Hawk was to discover why it is he fights, why he swings his sword. To do this he must of course defeat Griffith who originally won his allegiance in a duel. The difference between the two men's swords couldn't be more stark: Griffith's is slender and pointed with an ornate handle while Guts' is nothing more than a slab of metal with a handle. Even the two's fighting style is a reflection of their personality: Guts swings and bludgeons scattering men from their horses, Griffith jabs and slices with precision whether that's Zodd's demonic form or a pederast lord.
Fair to say then that Guts' sword is an integral part of him. Not only facing off against his foes and reflecting his personality but his raison d'etre, why he lives to this day and why he continues to live despite all that aligns against him. For Guts', there is never to be any rest, no white-picket fence and charming homestead waiting for him because his battle will never be over, regardless of what the alternate reality fever dream at the climax of the series implies.
The final battle is with himself though; Zodd, in their second encounter, refers to the Dragonslayer as a "truly demonic blade" and it becomes increasingly necessary for Guts' to slip further into the red mist of his inner demons to defeat his foes. The progression of the sword is the same as the horrors Guts' has faced, the most traumatic the murdering of a child, a loss of innocence as the once righteous sword turns from a means for survival to a weapon of slaughter.
The last piece to Guts' sword then is not the outer appearance, how it is used or what it represents, it's what is beneath the blade and subsequently inside Guts': a maelstrom of energies and complexities that can even strike at enemies incorporeal but is, when all's said and done, inhuman.
Fundamentally, Guts' sword is a character all its own, not a ridiculously oversized phallic analogy but a blade that speaks volumes (quite literally) about its wielder and more than words perhaps ever could.