Battered, rusting and smeared with dirt, the Volkswagen van could hardly be more clapped out. But spilling out of its back door are 24 sledges, surging across the ground with a sense of urgency. Each sledge carries a torch, a lump of animal fat and a roll of felt - equipment to aid the fight for survival. By inscribing his own surname on the van, above a darkened yet still visible red cross, Joseph Beuys announced the personal significance of this immensely powerful work. He called it The Pack, and the sledges certainly suggest an emergency team of dogs rushing across empty terrain to rescue a stranded victim. Although this piece was made back in 1969, the felt looks astonishingly pristine, its freshness making the van seem even more redundant.

Beuys claimed he had good reason to believe in primitive ways of healing. In 1943, at the age of 22, he was a Luftwaffe combat pilot flying over the Crimea. Hit by Russian flak, Beuys crash-landed in a snowstorm and was thrown free of the wreckage. He could easily have died, like his companion trapped in the smashed-up plane. According to Beuys, however, a miracle occurred. Some no-madic Tartars discovered him days later. He described, with understandable wonder, how they took him to a tent, covered his body in fat to help it generate warmth, and wrapped it in felt "as an insulator to keep the warmth in".

Nobody today can disentangle fact from legend in Beuys's arresting account of his struggle for life. But everyone can understand the overwhelming importance of this Lazarus-like recovery. It shaped the character of the art he produced after studying sculpture at the Kunstakademie Dusseldorf between 1947 and 1952. Three years later, the trauma involved in looking back at his career as a Nazi pilot triggered a serious psychological breakdown. For a while, he worked quietly on a farm owned by boyhood friends. By 1960, however, Beuys was ready to start defining his direction as the most charismatic, provocative and influential German artist of the postwar period.

As The Pack makes clear, he was preoccupied with the notion of sculpture's redemptive potential, helping to heal the wounds suffered by so many during that protracted and, on many occasions, bestial conflict. Guilt must have played a part in driving Beuys forward with such energy and resolve. Yet there is never any sense, in the moving show of his work at Tate Modern, that he used art as a facile means of comforting himself. Quite the reverse: the prevailing mood is of relentless pain.

One room is occupied by a desolate work called Show Your Wound, which was first installed in a dingy and depressing passage beneath the streets of Munich 30 years ago. The original location was grimly appropriate. A pair of dissection tables stand in a corner. Although both tables are bare, the fat-filled containers below suggest that bodily fluids have somehow been drained into them. We have no desire to linger here: the entire "environment" seems burdened with memories of the obscene horrors perpetrated, in the name of medical research, by fascist doctors during the Holocaust. Beuys was one of the earliest German artists to insist that these crimes should be confronted. He wanted the whole nation to face up to its responsibility for the barbarity of the death camps.

That is presumably why two large blackboards dominate the central wall in Show Your Wound. Beuys often resorted to drawing and writing with chalk, and was not shy of performing in public. The first time I saw this gaunt figure in his beaten-up felt hat, at the Tate in 1972, he was talking animatedly while scrawling diagrams and slogans on blackboards. His personal magnetism seemed as boundless as his energy. The people who listened to him then were probably more fascinated by the man than by his utopian political ideas.

The present exhibition proves that Beuys was able to transfer the forcefulness of his "actions" to his "environments", and nowhere more memorably than in Tram Stop. The origins of this work can be traced back to the artist's childhood memories of waiting for a tram to take him to school, when he used to sit on a historical monument in the centre of Cleves. Four 17th-century shell cases were clustered round the base of a cannon, from whose dragon-shaped mouth a cherub once sprang, symbolising the victory of love over war. In Tram Stop, however, Beuys replaced the cherub with a man's yelling head. I shall never forget seeing the original version in the German Pavilion at the 1976 Venice Biennale. Beuys insisted that the building's interior should be left in its dilapidated state, and a stretch of tramline led towards an iron cast of the cannon's vertical barrel. On top, the anguished head acted as a memorial to the victims of armed conflict, and yet it also implied that the mouth of war would one day be stopped.

This stark sculpture is the most impressive work by Beuys I have seen. But because he decided that, on all subsequent occasions, it would be displayed as a sequence of separate elements on the ground, the work's original meaning has been altered. The cannon looks felled; war itself seemingly vanquished. And the screaming head appears far more helpless lying back on the floor, which also brings it far closer to the basalt blocks strewn so dramatically across the ground in another piece called The End of the 20th Century.

At first sight, these blocks look like the petrified carcasses of creatures that died in some primordial catastrophe centuries ago. This is a memento mori of monumental proportions, and we pick our way through the sculpture as gingerly as visitors exploring remains scattered over a battlefield. Then, suddenly, we notice that these boulder-like forms are strangely alert. Although Beuys gouged a hole out of each block, he afterwards dressed the wounds with insulating clay and felt. This re-enactment of his own rescue by the Tartar nomads reaches its climax with Beuys's careful replacement of all the stone plugs he had cut out. They resemble eyes, and give the gathering an air of expectancy.

Beuys favoured basalt because of its volcanic origin, and The End of the 20th Century seems galvanised by a latent sense of dynamism. The tension between the slabs' aura of death and their equally strong capacity for life gives the work its primal power. While we recognise the mournful strain in a sculpture dedicated to the memory of everyone stricken by the ferocity of that century's murderous conflicts, the basalt blocks seem about to stir. Even as Beuys turns the work into a melancholy act of remembrance, he allows the fallen stones to hold out the promise of rebirth.

"Joseph Beuys: actions, vitrines, environments" is at Tate Modern, London SE1 (020 7887 8888) until 2 May