What does mean: She said her landlord was so mean that she would mind mice at crossroads ?
If you're curious about the literal meaning of "so mean that she would mind mice at crossroads" from which the saying derives its metaphorical usage, first you need to realize that mean is used in the sense of "extremely frugal, cheap, stingy, or penurious" (see merriam-webster.com definition 5a for mean (adj.)]), and mind is used in the sense of "to pay attention to" or "to be careful or cautious about" (see, for example, merriam-webster.com definitions 4a and 7 of mind (v).)
So the intent of the saying is to convey that the person is extremely careful, cautious, and attentive when they think about spending money—so much so that it's the same as if, when crossing a road, they look for anything as small as a mouse coming their way, and won't take the risk of crossing if there is one.
Is appears to be an Irish saying whose meaning depends on context. Generally, as in your example, it refers to a tight, stingy person.
A tight or miserly person who wouldn't want to part with there money.. can also refer to a quite and reserved person or in other slang terms, a 'dry' person.