As Professor Joad* might have said, that depends on what you mean by mind and being. However, to attempt detailed answers to these important but subsidiary questions would create an interminable delay in answering the main question posed. The approach here will be to allow the meaning of these two terms to emerge as a consequence of the discussion of the relationship between them. Before attempting this it would be useful to investigate the general form of the question and what the relationship between one entity and another means.
Relations may be of many kinds, including spatial, temporal, logical, mathematical, legal or just the usual anthropic ones, like love or hate. The relationship between an individual mind and an individual being can be explained as a precursor to tackling the more general question posed. One might meaningfully say, "John's mind is devoted to the study of philosophy". Alternatively, this could be expressed as, "John's mental activity is largely concerned with philosophy". This is like saying "John uses his computer mainly to gather information from the Internet." In the first two cases, 'mind' refers to a mental process that takes place in space and time in the region of John's brain. The object of john's thought (philosophy) is a body of knowledge that may take many forms, including processes in John's brain or memory as well as libraries of information.
The characteristic of the relationship between an individual mind and the objects of its thoughts looks like a one-many relation. If we say, "John chases after many women", the beings referred to belong to the class of women and 'chases after' is one of John's activities (when he's not doing philosophy). In this example, it is clear that it is John's whole being (including his mind) that is pursing physical bodies, unless he is just stalking them on the Internet. The sentence, "John's mind is filled with thoughts about women", provides an example of the relationship between an individual mind and female human beings, but this is a non physical relationship.
When John is pursuing philosophy, he may well be thinking about the concept of mind, as opposed to his individual mind. In so doing, one could reasonably say that he is creating a relationship within his own mind about the more abstract notion of mind in general. This would be a relationship between an individual mind and the concept of the class to which John's mind belongs. If we grant being to the hypothetical John, his thoughts would be an example of an individual being bound in a relationship with the concept of mind. However, this temporary bond can be described as being a certain kind of thought present in John's brain.
Mind has been implicitly defined above as the general name for thoughts and also for the capacity to generate such thoughts by a human individual. The existence of such thoughts depends upon the existence of the thinker (John) and on the mental processes, conscious or otherwise, taking place within his brain. John's individual being, therefore, is a necessary condition for the existence of John's thoughts and his mind.
In the example above, it is clear that mind is subordinate to the being of the individual possessing that mind. In general, the existence of human beings is necessary to the existence of human minds or what can reasonably be defined as the class of minds. The word 'mind', therefore, refers to the class of human minds, which clearly depends on the existence of the human race.
The initial question can now be answered. The relation between mind and being is just the class of possible relations between the class of human minds and the class of beings in general. In this formulation we have arrived at a many-many relation of the greatest diversity and complexity, the very opposite of what one might have expected from a metaphysical reduction of the question. However, no definition of being in general has been evoked other than the sum of beings involved in human thoughts.
Boiling the question down, one could say, "The relationship between mind and being comprises the totality of human thoughts about the world". This would necessarily include all erroneous thoughts as well as those that are generally held to be true. Indeed, one might contend that there are no absolutely true thoughts about beings, as opposed to the pure entities of mathematics and logic, so that the relationship between mankind and being in general is founded on approximate knowledge at best and complete delusion at worst.
* Cyril Edwin Mitchinson Joad (August 12, 1891 - April 9, 1953) was an English philosopher and broadcasting personality.