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.
Mrigshira - Mrigshira is nakshatra of desire oriented people. Someone who is keep searching for his next desire satisfaction. It is a nakshatra of disguise too. It is also related with Spying or Stalking and travelling. Please read this to get detailed info about Mrigshira - https://www.astrosaxena.com/mrig.
Taurus - As Mrigshira is part of Taurus, Taurus sign and its representations become important here. Taurus is the 2nd sign of zodiac belt, so it represents many things related with 2nd house of horoscope like, Hoarded Wealth, Assets, Savings, Finances, Luxuries and Liquid Money. All in all a sign related with luxuries and all the conveniences of life. Taurus is consisted of 2 and half Nakshatras, i.e. Krittika, Rohini and Mrigshira. Taurus' lord is Venus.
Gemini - As Mrigshira is also a part of Gemini, Gemini sign and its representations become important here. 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.
Venus – As Venus rules Taurus, Venus’ position and dignity is important to know about the overall functioning of any planet in Mrigshira/Taurus.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Mars - As Mrigshira is ruled by Mars, Mars's position and dignity will also have an important role in functioning and results of any planet in Mrigshira.
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 Mrigshira Nakshatra – When Mars is in Mrigshira Nakshatra, it is in own nakshatra. So, nakshatra-wise Mars is in good dignity. Although in Taurus portion, it is in neutral sign and in Gemini portion, it is in enemy sign. So, this position can work better with Mars in Taurus. As Mars represents actions & efforts and Mrigashira is nakshatra of searching, it shows that they can be very good at research related activities. They can put all their efforts in researching hidden things. As Mrigashira's mythological story is related with sexual intercourse, they can have high sexual drive. In Taurus section, they seek security through their actions but Gemini action is more about making efforts in things of interests and skills. This placement can be troublesome in Gemini for a few reasons, i.e. their efforts can get scattered everywhere and may not be aligned in one direction and they can have a very harsh or stinging way of speech. At the same time, they can be business driven and approach business matters like a battle to win. Overall, it is a good position for business or any kind of research work but the biggest challenge with this position is to streamline efforts in one direction and not to waste energy in scattered directions.
Role of Venus – Venus's position will become important in functioning and results of Mars in Mrigshira/Taurus as Venus rules Taurus. If Venus is in good dignity then Moon will have proper direction.
Role of Mercury – Mercury's position will become important in functioning and results of Mars in Mrigshira/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Moon will have proper direction.
Role of Mars - As we are trying to interpret Mars only, we need not to look at Mars's position and dignity separately.
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 Mrigshira. 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 Mrigshira can work in a chart.