Let’s look at important things here –
Mars - Mars represents our will power, courage, ability to take actions, aggressive nature, anger, our fighting ability, brother, male friends, a boy friend for a girl, a soldier, an athlete and real estate etc.
Punarvasu - It is a nakshatra of rehabilitation and recovery process. It is very closely connected with after-care medical activities. It can also be a nakshatra of counselling. For more information on Punarvasu Nakshatra, please check this - https://www.astrosaxena.com/punnaksh.
Gemini - As Punarvasu is part of Gemini, Gemini sign and its representations become important when any planet is in Punarvasu/Gemini. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Cancer - As Punarvasu is also a part of Cancer, Cancer sign and its representations become important when any planet is in Punarvasu/Cancer. Cancer is 4th sign of Zodiac Belt, hence it represents the things represented by 4th house like Mother, Mother's Care, Emotions, Taking Care of Others and Nourishment etc. Cancer is consisted of 2 and half Nakshatras namely Punarvasu, Pushyami and Ashlesha. Cancer's lord is Moon, which again represents almost same things which Cancer and 4th house represents.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Punarvasu/Gemini.
Moon - As Moon rules Cancer, Moon's position and dignity is important to know about the overall functioning of any planet in Punarvasu/Cancer.
Jupiter - As Punarvasu is ruled by Jupiter, Jupiter's position and dignity will also have an important role in functioning and results of any planet in Punarvasu.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Mars in Punarvasu Nakshatra – Now, the actions and efforts of Mars are coming in to the nakshatra of rehabilitation and recovery. So, prima-facie these people can be involved in any kind of rehabilitation or recovery work where they serve people recovering from turmoils and chaotic events of life. So, they can be seen as Soldiers, Doctors, Rehabilitation Workers etc. The difference between Gemini sign and Cancer sign will be that Mars in Gemini can serve people in recovering through their business & communication and Mars in Cancer can be about going into difficult zone directly and putting the efforts. So, Mars in Punarvasu/Gemini can be more like counselors whereas Mars in Punarvasu/Cancer can be more like someone helping people directly in troublesome scenario. Sign-wise, Mars is weak in both Gemini and Cancer but Mars in Cancer is more troublesome as Mars is weakest there. They need to take care that they should not wrongly use their aggression or anger. Mars in enemy sign or debilitation sign is always the most difficult positions to interpret as they can become criminal and police both. Lots depend on upbringing of person and position of sign lord and nakshatra lord. It shows whether they will utilize Martian energy positively or negatively.
Role of Mercury – Mercury's position will become important in functioning and results of Mars in Punarvasu/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Mars will have proper direction.
Role of Moon – Moon's position will become important in functioning and results of Mars in Punarvasu/Cancer as Moon rules Cancer. If Moon is in good dignity then Mars will have proper direction.
Role of Jupiter - Likewise, Jupiter's placement is important to guide Mars in right direction, being Punarvasu's lord.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Mars in Punarvasu. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Mars in Punarvasu can work in a chart.
Hope this helps. Please post any comment or query you may have.