Little has been found directly relating to Mary's life other than the basics. It's been proliferated across the internet that she died on 13 February 1736/7, based, apparently, on one person's misreading of a record made by Rev. Hale of Beverly (which is transcribed correctly and included in the published vital records of Beverly). Hale ocassionally put a day and month before the year of someone's death, but for the most part, he did not. Researchers have misinterpreted this as indicating that everyone whose name appears after a full date died on that date. This would suggest very strange goings-on in Beverly. Hale's record shows only that she died in 1737.1 After her husband died, she sent this document to John Appleton, Judge of Essex County Probate.2 It's a little atypical in that it isn't from the executors themselves, but the widow, mentioning her need for subsistance money:

These comes to informe your honor that I the subcriber desier that the last will and testament of my late husband Edward Dodge of Beverly deseased may be approved for I have agreed with my two sons Edward and Marke Dodge which are exers to sd will and have taken bond for my maintenince so rest your servant to command.

Although she probably didn't write the letter herself, she did sign it with her name, and in a confident hand.
     Edward was unusually specific in his will about how much care should be taken of Mary after his death. He wanted her to have the use of "my best feather bed, boulster & two pillows & the furniture belonging to the same, two pair of sheets, four pillow cases, two table cloaths & twelve napkins, four towells, an Iyron, pott & hooks, a brass skillett, two puter platters & two puter plates, my oak chest & a pine box to bee free to her own disposall as she pleaseth and it is my mind & will that my two sons...do take the care of her my said beloved wife & carefully & sutably provide for her as her case may require & provide for her a gentle, sutable hors to ride on & a sutable person to attend to cary her abroad when she shall have occasion, & to provide for her all other things that may be necessary."

Children of Mary Hascoll and Edward Dodge:

i. Mary, b. 21 Apr. 1675
ii. Jonathan, b. 3 July 1679
iii. Edith, b. 3 Jan. 1680/81
iv. Ruth, b. 15 Aug. 1685
v. Edward, bap. 6 Nov. 1687
vi. Hannah, bap. 17 Apr. 1692
vii. Mark, bap. 21 Oct. 1694

vital records sources: Vital Records of Beverly, Massachusetts, to the end of the year 1849, vol. 2 (Marriages and Deaths) (Topsfield, MA: Topsfield Historical Society, 1907), 90, 419. The marriage record says "last Aprill." The death record is taken from Rev. Hale's account of deaths in Beverly, listed with others as having died in 1737. No day or month is given for her record.

1. see vital records sources.
2. Essex Co., MA, probate file 7825, 8 Mar. 1726/7. He wrote his will on 17 Feb. 1714/5.