Hi Lauren,
More than mouth cancer, I would attribute it to the minor esophageal variceal tear that could have possibly occurred.
To stop the bleeding, we need to find the cause of it. If it is due to esophageal tear, then the bleeding veins are to be ligated surgically.
If it is a primary bleed from the mouth, it may be due to aphthous ulcer in view of his general condition. In that case,
multivitamin supplements will help him.
Pressure compresses can be used locally to arrest the fresh bleeding.
If it is due to mouth cancer, then again, management will be surgical.
These are only my broad views.
A physical examination would be ideal to know the cause.
Hope this helps.
Regards,