verb

• (archaic) To soil with mud or a similar substance.
  "The Minde, constrain’d the Bodies want to feele, Makes Salves of Earth the Bodies hurt to heale, Which doe the Mind bemire with thoughts vnfitt;"
• (archaic) To immerse or trap in mire.
  "True, there are by the direction of the Law-giver, certain good and subs[tantial] Steps, placed even through the very midst of this Slough; but at such a time as this place doth much spue out [its filth] as it doth against change of weather, these steps are hardly seen; or if they be, Men through the diziness of their heads, step besides; and then they are bemired to purpose, notwithstanding the steps be there […]"
• (figurative) To stain or mar, as with infamy or disgrace; to tarnish; to sully.
  ""We have to stop him at any cost. That is the way our Cause gets bemired. Some villain who knows nothing about it comes into it for money and so the labours of the honest mediums get discounted.""