Many questions as to wether women should recite or chant some mantras, or not. As a matter of fact the Vedic Scripts don't discriminate women.

Many questions as to wether women should recite or chant some mantras, or not. As a matter of fact the Vedic Scripts don't discriminate women. On the contrary, womanhood is held in the Highest Esteem, and women are respected as Maa, (Mother) irrespective of their age and status. Every woman is effortlessly spiritual when they chose to be so. As mothers, daughters, sisters and wives they are unmatched in every noble quality. She is Shakti, very manifestation of the Divine Feminine. Or Kali dancing wildly on the prone body of Shiva. She is Prakriti, without whom Purusha would be immaterial. Those who have actually felt the presence of the Divine would never bother with these social constructs. 
The Vedas, Puranas and mantras are embodiments of the god. The unspoken secret that accompanies every mantra is that the absolute fullness of a mantra can be experienced by the one who chants it only when there is purity in thought, word and deed. Now purity here means cleanliness of body and mind and soul. In olden days cleanliness and discomfort was a major issue. So basically women in the earlier age were advised not to perform worship or chant any mantra when they had their menstruating cycle of the month. They were encouraged not to take part in any religious ceremony. Due to modern technology this is not an issue today. Fatigue, Pain and distress are real issues then and now. But women are no longer excused from house work, office work, studies, commuting, serving others and so on during this period. Earlier menstruating women were not allowed in the kitchen, in the temple or In the puja room. It was not about women being banned from the kitchen. In those days when a woman was menstruating she actually had to stay in her own room. ‪Later on she was allowed out of her room, but couldn't enter the kitchen. Now she can enter the kitchen. As the beliefs slowly change. But actually this is not done for any reason of prejudice but for cleanliness. Because they were considered as unclean and impure during menstruation. People believed that food gets dirty and inedible if a woman touches it who is currently menstruating. While She performs puja or chants mantra, she is not clean enough to go near God. So she was prohibited by Pandits. Also Its believed that some of the Vedic Verses vibrations are so powerful in nature. Once a woman starts chanting these verses regularly, it might cause hormone disturbances in the body's physical mechanism and disturb their menstrual cycle. 
Well In my opinion you can chant the name of Lord anytime and just anywhere, with or without beads. The Maha Mrityunjaya Mantra or any other powerful mantra can be chanted by anybody. The most important aspect is to understand the meaning of this mantra word by word before chanting it. That’s because by knowing the meaning, one can easily contemplate on the aspect of birth and death cycle.
And Lord sees your devotion, faith and sincerity. He sees if ur inner self is pure or not , not the physical body. So as long as woman stays clean and takes adequate rest, and as long as she is not distressing herself emotionally and physically, as long as she can focus her mind on God, performing puja visiting temples and chanting mantras should be fine. No Sin will Accrue to Her! Jai ShivaShakti!!