専用の機能は提供しておりませんが、以下のようにクリップボード機能による対応が考えられます。

Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
    ' コピー元シートの設定
    Dim bc As New FarPoint.Win.Spread.CellType.ButtonCellType
    bc.Text = "Click!"
    FpSpread1.ActiveSheet.Cells(1, 0).CellType = bc
    FpSpread1.Sheets(0).Cells(1, 1).Value = "test"
    FpSpread1.Sheets(0).Cells(1, 1).BackColor = Color.LavenderBlush
End Sub

Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
    ' fpSpread1のシートをコピーしてfpSpread2に追加する
    copySheet(FpSpread1)
    pasteSheet(FpSpread2)
End Sub

Private Sub pasteSheet(ByVal TestFpSpread As FarPoint.Win.Spread.FpSpread)
    Dim spreadView As FarPoint.Win.Spread.SpreadView = TestFpSpread.GetRootWorkbook()
    Dim action As FarPoint.Win.Spread.Action = spreadView.GetActionMap().[Get](FarPoint.Win.Spread.SpreadActions.ClipboardPasteSheet)
    If TypeOf (action) Is FarPoint.Win.Spread.UndoRedo.UndoAction Then
        action = (CType(action, FarPoint.Win.Spread.UndoRedo.UndoAction)).Clone()
    End If
    If (action IsNot Nothing) Then
        If spreadView.AllowUndo AndAlso TypeOf (action) Is FarPoint.Win.Spread.UndoRedo.UndoAction Then
            spreadView.UndoManager.PerformUndoAction(CType(action, FarPoint.Win.Spread.UndoRedo.UndoAction))
        Else
            action.PerformAction(spreadView)
        End If
    End If
End Sub

Private Sub copySheet(ByVal TestFpSpread As FarPoint.Win.Spread.FpSpread)
    Dim spreadView As FarPoint.Win.Spread.SpreadView = TestFpSpread.GetRootWorkbook()
    Dim action As FarPoint.Win.Spread.Action = spreadView.GetActionMap().[Get](FarPoint.Win.Spread.SpreadActions.ClipboardCopyActiveSheet)
    If TypeOf (action) Is FarPoint.Win.Spread.UndoRedo.UndoAction Then
        action = (CType(action, FarPoint.Win.Spread.UndoRedo.UndoAction)).Clone()
    End If
    If (action IsNot Nothing) Then
        If spreadView.AllowUndo AndAlso TypeOf (action) Is FarPoint.Win.Spread.UndoRedo.UndoAction Then
            spreadView.UndoManager.PerformUndoAction(CType(action, FarPoint.Win.Spread.UndoRedo.UndoAction))
        Else
        action.PerformAction(spreadView)
        End If
    End If
End Sub

private void Form1_Load(object sender, EventArgs e)
{
    // コピー元シートの設定
    FarPoint.Win.Spread.CellType.ButtonCellType bc = new FarPoint.Win.Spread.CellType.ButtonCellType();
    bc.Text = "Click!";
    fpSpread1.ActiveSheet.Cells[1, 0].CellType = bc;
    fpSpread1.Sheets[0].Cells[1, 1].Value = "test";
    fpSpread1.Sheets[0].Cells[1, 1].BackColor = Color.LavenderBlush;
}

private void button1_Click(object sender, EventArgs e)
{
    // fpSpread1のシートをコピーしてfpSpread2に追加する
    copySheet(fpSpread1);
    pasteSheet(fpSpread2);
}
private void pasteSheet(FarPoint.Win.Spread.FpSpread TestFpSpread)
{
    FarPoint.Win.Spread.SpreadView spreadView = TestFpSpread.GetRootWorkbook();
    FarPoint.Win.Spread.Action action = spreadView.GetActionMap().Get(FarPoint.Win.Spread.SpreadActions.ClipboardPasteSheet);
    if ((action) is FarPoint.Win.Spread.UndoRedo.UndoAction)
        action = ((FarPoint.Win.Spread.UndoRedo.UndoAction)action).Clone();
    if ((action != null))
    {
        if (spreadView.AllowUndo && (action) is FarPoint.Win.Spread.UndoRedo.UndoAction)
            spreadView.UndoManager.PerformUndoAction((FarPoint.Win.Spread.UndoRedo.UndoAction)action);
        else
            action.PerformAction(spreadView);
    }
}

private void copySheet(FarPoint.Win.Spread.FpSpread TestFpSpread)
{
    FarPoint.Win.Spread.SpreadView spreadView = TestFpSpread.GetRootWorkbook();
    FarPoint.Win.Spread.Action action = spreadView.GetActionMap().Get(FarPoint.Win.Spread.SpreadActions.ClipboardCopyActiveSheet);
    if ((action) is FarPoint.Win.Spread.UndoRedo.UndoAction)
        action = ((FarPoint.Win.Spread.UndoRedo.UndoAction)action).Clone();
    if ((action != null))
    {
        if (spreadView.AllowUndo && (action) is FarPoint.Win.Spread.UndoRedo.UndoAction)
            spreadView.UndoManager.PerformUndoAction((FarPoint.Win.Spread.UndoRedo.UndoAction)action);
        else
            action.PerformAction(spreadView);
        }
    }