This is a hard question to answer. Generally dasatinib is well tolerated. In the first few weeks, some patients may have headaches or vague abdominal discomfort but this usually resolves. Long term, as is well known, you need to watch out for the pleural effusions or very very rarely the pulmonary arterial hypertension that has been associated with the use. Obviously no two patients are the same and there may be some issues that one patient may have that are not common. As you point out, you need to distinguish between a dasatinib side effect and something else. Rather than reduce the dose, I would be tempted to hold drug for a week or so and see if the symptoms improve. It should not take much longer than this to determine where you stand and then you can decide about rechallenging and whether at full dose or a slightly reduced dose initially, planning to increase the dose in the near future.
Despite how good TKI therapy, some patients just cannot cope with the diagnosis and thought of perhaps lifelong therapy. Given that in the case of both imatinib and dasatinib, there were GI side effects here, I would consider gastroscopy to rule out some upper GI pathology. Also keep in mind, not uncommonly, our patients are or get depressed and that may require intervention.