You can specify that the tests must execute sequentially by adding sequential to your specification.
If you are using unit style testing, put the statement sequential in a line above your tests (examples borrowed from specs docs):
  import org.specs2.mutable._
  class HelloWorldSpec extends Specification {
    sequential
    "The 'Hello world' string" should {
      "contain 11 characters" in {
        "Hello world" must have size(11)
      }
      "start with 'Hello'" in {
        "Hello world" must startWith("Hello")
      }
      "end with 'world'" in {
        "Hello world" must endWith("world")
      }
    }
  }
If you are using acceptance style testing, just add sequential inside the definition of is
 import org.specs2._
  class HelloWorldSpec extends Specification { def is =
    sequential                                                      ^
    "This is a specification to check the 'Hello world' string"     ^
                                                                    p^
    "The 'Hello world' string should"                               ^
      "contain 11 characters"                                       ! e1^
      "start with 'Hello'"                                          ! e2^
      "end with 'world'"                                            ! e3^
                                                                    end
    def e1 = "Hello world" must have size(11)
    def e2 = "Hello world" must startWith("Hello")
    def e3 = "Hello world" must endWith("world")
  }
As a side note, you are probably getting the stack overflow errors from an error in your software, rather than the tests being too long.