Can monster energy drink possibly cause severe joint pain and depression?

Energy drink: Depending on the quantity consumed & the frequency of use, it is possible.

Yes: These drinks are stimulants. Stimulants often do exacerbate pain on their own. They can also cause both mood and perceptual problems, including depression, or dysphoria. The link between depression and pain, specifically that each makes the other feel worse, is well known, so it is not surprising that a stimulant would cuase or exacerbate both. Severe joint pain is not however typical.