May be you need two forms one for each action. Use two forms for each action e.g.
@(using Html.BeginForm("Method For Update", "Controller Name", FormMethod.Post))
{
}
@using(Html.BeginForm("Method For Delete", "Controller Name", FormMethod.Post))
{
}
if you need only one then for delete purpose use ajax as recomended by Rahul Rajat Singh.