Was it a way to take an arrow out of wound safely in Medieval Time?

Your question is certainly not weird, but well received :-) There are many depiction of bad-ass medieval heroes pulling out arrows from their bodies to carry on their good fight. It is quite the trope in movies relating the life of Joan of Arc. However, there is quite a good reason for that.

There are many accounts of wounded people in medieval chronicles and narrative sources. Sometimes it's a spear in the shoudler, other times it's a canon ball in the leg. Why people survived those wounds seems often random. I found it to be rare for someone to die on the spot from such an injury. It is more often than not followed by several days of pain and suffering that either lead to a full recovery or death. Chroniclers are very scarce on medical details.

Would you believe it? It so happens that Joan of Arc was hit not once, but twice, by arrows. The first time while liberating Orléans, the second time while besieging Paris. The first wound really made a strong impression on her contemporaries for she predicted it. In a letter dated from the 22th April 1429, a counselor to Philip the Good, duke of Burgundy (Joan's enemy), wrote to his master a letter reporting Joan's injury prediction. However, she only arrived in Orléans a week later and she was hit, while attacking the Tourelles, on May 6th!

How did she foresee her injury? No one knows. Her judges upon her trial at Rouen tried to trap her. They asked if she insured everybody's safety in Charles VII's army. Her answer was cristal clear. She said "No". She knew from the start that people would be injured or killed and she never ever claimed otherwise. Nevertheless, she was considered as a lucky charm--but that drives us away from the topic at and and back to her natural charisma.

When Joan of Arc was hit at the battle of the Tourelles, she performed heroically. She was driven away to the back of the army. People offered her "charms" (meaning magical ailments) but she refused them all. Instead, she asked for a bit of olive oil, some cotton and grease. She'd been hit in the neck or very close to it! Nevertheless, she pulled the arrow out with no more than a bit of olive oil, some cotton and grease to help her. There are too many accounts of this event for it to be discarded as fiction. We need to consider it true. Dunois reported in 1456 that the arrow (maybe an arbalest bolt) had entered half a foot (15cm or 6 inches) deep into Joan's flesh.

Not only that. Once she pulled the arrow out... she returned to battle! At that point, everybody was sure by that the day was lost. She discarded those feelings, pushed through and galvanized the troops. Her banner was raised again near the walls of the Tourelles by two valiants men who dared and challenged death to recover it. The French rushed towards Joan's banner, attacked the Tourelles from that spot as she pointed towards it and they won the fortress back from the English! As they attempted to flee, the English officers actually fell into the water of the Loire river and drowned when a demolition ship exploded under their feet as they were crossing the drawbridge. According to an Italian chronicler, that demolition ship had been prepared on Joan's initiative.

We have less details regarding Joan's second injury at the siege of Paris. We know she was hit in the leg. She must have taken care of it somehow for she was still under the walls of Paris when the day turned to dusk. She just wouldn't leave or quit! The duke of Alençon, whom she promised earlier that he'd come back safely to his wife, personally came to snatch her away from the battlefield that night. A few months earlier, Joan had also been hit from a rock on the head at Jargeau while climbing siege ladders. Nevertheless, she woke back up and jumped back into the fight, as if nothing had happened.

Though Joan of Arc never quit the battlefield, it took her two weeks to recover from her first arrow injury and five days to recover from the second. About that second injury, she actually wrote a letter to the people of Troyes, on September 22th, 1429, to report on her speedy recovery.

As stated before, those types of wound came with a time stamp. Who would survive and why seems like a mystery from our contemporary perspective. However, barbers (yes, people who cut your hair and beard) were often called upon to heal grave injuries. Since Latran (1215), clerics were forbidden to indulge into any manual activity. That's why artisans were deemed more suited to the task of surgery. What those barbers knew about human anatomy and how to heal traumas? I think we'll never know...