This research study is for people with a specific type of leukemia called Philadelphia chromosome positive acute lymphoblastic leukemia (the type the patients have). The investigators plan to give you combination of 3 drugs (dasatinib, mitoxantrone, cytarabine) for the first part of the chemotherapy (called Induction). The investigators have previously shown that the combination of mitoxantrone and cytarabine is very effective in your kind of leukemia. The purpose of this study is to establish a safe dose range of dasatinib in combination with this standard induction chemotherapy based on side effects. If possible, the trial will also give us an idea of how well this combination might work in treating your leukemia. Previous studies have shown that dasatinib can produce responses when given alone for your kind of leukemia. By using the dasatinib together with the chemotherapy, the investigators believe that we can kill even more leukemia cells than with either treatment alone. The investigators will initially treat patients with a low dose of dasatinib and monitor for side-effects. If the initial group of patients is able to tolerate this low-dose of dasatinib, then future patients will receive higher doses of dasatinib. Mitoxantrone and cytarabine chemotherapy is the standard therapy at the investigators' institution for the patient's leukemia and it is the combination of dasatinib with this chemotherapy that is new and investigational in this study.

Inclusion Criteria:

• Previously untreated and treated adult patients (> or = 18 years old) with a diagnosis of:

  • Philadelphia-chromosome positive acute lymphoblastic leukemia
  • Lymphoid blast crisis of known chronic myelogenous leukemia NOTE: Patients must have evidence of a t(9;22) in leukemic cells based on chromosomal or molecular analysis.

NOTE: The diagnosis must be confirmed by the pathology department at MSKCC. NOTE: It is recognized that newly diagnosed patients may be started on therapy with cytarabine and high-dose mitoxantrone (which is the standard of care at our institution for treating adult ALL) prior to the identification of t(9;22) in leukemic cells. These patients will remain eligible for participation on study and will be evaluable for response if it is possible to start treatment with dasatinib within 30 days of receiving induction chemotherapy.

• Patients with adequate hepatic function (AST and ALT < or = 2.5 the institutional ULN, bilirubin < or = 2.0 mg/dl).
• Patients with adequate renal function (creatinine < or = 2.0 mg/dl or creatinine clearance > 50 ml/min).
• Patients with an LVEF > or = 50%.
• Karnofsky performance status > or = 20%.
• Ability to take oral medication (dasatinib must be swallowed whole).
• Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (sensitivity > or = 25IU HCG/L) within 72 hours prior to the start of study drug administration. Persons of reproductive potential must agree to use and utilize an adequate method of contraception throughout treatment and for at least 6 months after study drug is stopped. Prior to study enrollment, women of childbearing potential must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an unintentional pregnancy.
• concomitant Medications: Patient agrees to discontinue St. Johns Wort while receiving dasatinib therapy (discontinue St. Johns Wort at least 5 days before starting dasatinib); Patient agrees that IV bisphosphonates will be withheld for the first 8 weeks of dasatinib therapy due to risk of hypocalcemia.
• Signed informed consent, which indicates the investigational nature of this study, within 30 days of treatment initiation, is required.

Exclusion Criteria:

• Female patients who are pregnant or lactating. Women and men of childbearing age should use effective contraception.
• Patients with uncontrolled active infections.
• Patients who are receiving other systemic chemotherapy. Patients must have been off prior antileukemic therapy for at least 2 weeks (hydroxyurea is considered acceptable).

NOTE: Patients who had previously received combination therapy with cytarabine, high-dose mitoxantrone and dasatinib will be excluded from the trial. All other prior therapies will be allowed, including prior tyrosine kinase inhibitors usage. Prior dasatinib use will be allowed (as a single agent or in combination therapy, other than the combination therapy with cytarabine and high-dose mitoxantrone).

• Concomitant active secondary malignancy requiring treatment (other than squamous cell and basal cell carcinoma of skin).

• Concurrent medical condition which may increase the risk of toxicity, including: grade ≥ 2 pleural or pericardial effusion.

• Cardiac Symptoms; any of the following should be considered for exclusion:

  • Uncontrolled angina, congestive heart failure or MI within (6 months).
  • Diagnosed congenital long QT syndrome.
  • Any history of clinically significant ventricular arrhythmias (such as ventricular - tachycardia, ventricular fibrillation, or Torsades de pointes).
  • Prolonged QTc interval on pre-entry electrocardiogram (> 450 msec).
  • Subjects with hypokalemia or hypomagnesemia if it cannot be corrected prior to dasatinib administration.

• History of significant bleeding disorder unrelated to cancer, including:

  • Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease).
  • Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies).

Ongoing or recent (< or = 3 months) significant gastrointestinal bleeding

• Concomitant Medications, any of the following should be considered for exclusion:

  • Category I drugs that are generally accepted to have a risk of causing Torsades de Pointes including: (Patients must discontinue drug 7 days prior to starting dasatinib)
  • quinidine, procainamide, disopyramide amiodarone, sotalol, ibutilide, dofetilide erythromycin, clarithromycin chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone, halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine.