Hi simflex,
You need to add Button outside gridview in your code. So please refer the below code and modify as per your requirement.
HTML
<asp:Button ID="btnIncone" Text="Save Income" CssClass="btnSuccess" OnClick="OnSaveIncome"
    runat="server" />
<asp:Button ID="btnSpouse" Text="Save Spouse" CssClass="btnSuccess"  OnClick="OnSaveSpouse"
    runat="server" />
C#
protected void OnSaveIncome(object sender, EventArgs e)
{
    SqlConnection con = new SqlConnection(contring);
    foreach (GridViewRow row in gvIncome.Rows)
    {
        string Message = (row.FindControl("txtspouseincome") as TextBox).Text.Trim();
        SqlCommand cmd = new SqlCommand("INSERT INTO TableName VALUES(@Message)", con);
        cmd.Parameters.AddWithValue("@Message", Message);
        con.Open();
        cmd.ExecuteNonQuery();
        con.Close();
    }
    this.SetInitialRow();
}
protected void OnSaveSpouse(object sender, EventArgs e)
{
    SqlConnection con = new SqlConnection(contring);
    foreach (GridViewRow row in gvIncome.Rows)
    {
        string Message = (row.FindControl("txtspouseincome1") as TextBox).Text.Trim();
        SqlCommand cmd = new SqlCommand("INSERT INTO TableName VALUES(@Message)", con);
        cmd.Parameters.AddWithValue("@Message", Message);
        con.Open();
        cmd.ExecuteNonQuery();
        con.Close();
    }
    this.SetInitialRow();
}
Vb.Net
Protected Sub OnSaveIncome(sender As Object, e As EventArgs)
	Dim con As New SqlConnection(contring)
	For Each row As GridViewRow In gvIncome.Rows
		Dim Message As String = TryCast(row.FindControl("txtspouseincome"), TextBox).Text.Trim()
		Dim cmd As New SqlCommand("INSERT INTO TableName VALUES(@Message)", con)
		cmd.Parameters.AddWithValue("@Message", Message)
		con.Open()
		cmd.ExecuteNonQuery()
		con.Close()
	Next
	Me.SetInitialRow()
End Sub
Protected Sub OnSaveSpouse(sender As Object, e As EventArgs)
	Dim con As New SqlConnection(contring)
	For Each row As GridViewRow In gvIncome.Rows
		Dim Message As String = TryCast(row.FindControl("txtspouseincome1"), TextBox).Text.Trim()
		Dim cmd As New SqlCommand("INSERT INTO TableName VALUES(@Message)", con)
		cmd.Parameters.AddWithValue("@Message", Message)
		con.Open()
		cmd.ExecuteNonQuery()
		con.Close()
	Next
	Me.SetInitialRow()
End Sub