We know from studying their remains, that woolly mammoths ate herbaceous plants (herbs), flowering plants, shrubs, mosses and matter from trees.
The woolly mammoth had evolved a “two-fingertip” trunk which enabled them to “pick up” and eat the short grasses and shrubbery that were a part of their diets in the last ice age. In comparison, modern elephants wrap their trunks around tall tufts of grass and yank them up.
We also know from studying the intestines of some frozen mammoths which have been recovered that they, particularly the younger ones, ate faecal matter. The most famous mammoth studied for this are the recovered frozen remains of a calf who has been named Lyuba, who is the world’s most preserved mammoth specimen and currently “resides” in a museum in Salekhard, Russia. The faecal matter, we believe, was digested, particularly by younger mammoths, to help promote intestinal microbes, which aided the digestion of heavy vegetation.
You can learn more about woolly mammoths by visiting the Wikipedia page.
I also recommend a book to you, called “Mammoths: Ice Age Giants”, by Adrian Lister. Click here to see it.
Here is a good one-hour long official National Geographic documentary on mammoths, which may interest you: