Adhesive molecules are suggested to play an important role when a single tissue is separated into two in developmental processes, illustrated by tissue-specific cadherins in the neural tube formation of amphibians. In this paper, we study the possibility for tissue separation to be carried out only by differential cell adhesion and random cell movement without any other morphogenetic mechanisms. We consider a two-dimensional regular triangular lattice filled with cells of three types (black, white, and gray). In the initial state, a cluster of black cells and a cluster of white cells are in contact and are surrounded by gray cells. Nearest-neighbor cells exchange their location at random, but the movement occurs faster if it increases the total adhesion. We considered separation to be successful if, in the final state, black cells and white cells kept their clusters but two clusters lost their direct contact with each other as gray cells are inserted between them. The maximum total adhesion (MTA) rule conjectures that the spatial pattern achieving maximum total adhesion might be that obtained in the final state. In the computer simulation, the runs for successful separation satisfied the condition predicted by the MTA rule. However, the condition for successful separation was more restricted than that predicted by the MTA rule. For some combinations of adhesions, it took an extremely long time to accomplish tissue separation. Finally, we discuss the role of homophilic adhesion molecules (such as cadherins) in the tissue separation processes, and show that the new expression of homophilic adhesion molecules cannot perform tissue separation without the change in other morphogenetic processes.