How to refresh jquery datatable without database call

A whole working demo to achieve your requirement for doing database call after client side add/remove operation:

Model

public class Student
{
    public int Id { get; set; }
    public string Name { get; set; }
    public int Age { get; set; }
    public string Grade { get; set; }
}
public class StudentChangesModel
{
    public List<Student> AddedStudents { get; set; }
    public List<Student> DeletedStudents { get; set; }
}  

View

@{
    ViewData["Title"] = "Student Management";
}

<h1>Student Management</h1>

<!-- Table to display students -->
<table id="studentsTable" class="display" style="width: 100%;">
    <thead>
        <tr>
            <th>ID</th>
            <th>Name</th>
            <th>Age</th>
            <th>Grade</th>
            <th>Actions</th>
        </tr>
    </thead>
</table>

<!-- Form to add a new student -->
<h2>Add New Student</h2>
<div>
    <label>Name: </label><input type="text" id="nameInput" />
    <label>Age: </label><input type="text" id="ageInput" />
    <label>Grade: </label><input type="text" id="gradeInput" />
    <button id="addStudentBtn">Add Student</button>
</div>

<!-- Button to save changes -->
<button id="saveChangesBtn">Save Changes</button>

@section Scripts {
        <script src="https://code.jquery.com/jquery-3.6.0.min.js"></script>
        <script src="https://cdn.datatables.net/1.11.5/js/jquery.dataTables.min.js"></script>
        <script>
            var addedStudents = [];
            var deletedStudents = [];

            $(document).ready(function () {
                var table = $('#studentsTable').DataTable({
                    ajax: {
                        url: '/Students/GetStudents',
                        dataSrc: ''
                    },
                    columns: [
                        { data: 'id' },
                        { data: 'name' },
                        { data: 'age' },
                        { data: 'grade' },
                        { data: null, defaultContent: '<button class="delete-btn">Delete</button>' }
                    ]
                });

                // Add new student to the table
                $('#addStudentBtn').click(function () {
                    var newStudent = {
                        id: 0, // Empty for new student
                        name: $('#nameInput').val(),
                        age: parseInt($('#ageInput').val()),
                        grade: $('#gradeInput').val()
                    };

                    // Add the new student to the DataTable
                    table.row.add(newStudent).draw();

                    // Track the new student in "addedStudents" array
                    addedStudents.push(newStudent);

                    // Clear input fields
                    $('#nameInput').val('');
                    $('#ageInput').val('');
                    $('#gradeInput').val('');
                });

                // Capture delete button click
                $('#studentsTable tbody').on('click', 'button.delete-btn', function () {
                    var row = table.row($(this).parents('tr'));
                    var data = row.data();

                    // Track removed students only if they exist in DB (have an ID)
                    if (data.id) {
                        deletedStudents.push(data);
                    }

                    // Remove the row from DataTable
                    row.remove().draw();
                });

                // Save changes to the server
                $('#saveChangesBtn').click(function () {
                    console.log(addedStudents)
                        console.log(deletedStudents)
                    $.ajax({
                        url: '/Students/SaveStudents',
                        type: 'POST',
                        contentType: 'application/json',
                        data: JSON.stringify({
                            addedStudents: addedStudents,
                            deletedStudents: deletedStudents
                        }),
                        success: function (response) {
                            addedStudents = [];
                            deletedStudents = [];
                            alert('Changes saved successfully!');
                            table.ajax.reload();
                        },
                        error: function (error) {
                            console.error('Error saving changes', error);
                        }
                    });
                });
            });
        </script>
}

Controller

public class StudentsController : Controller
{
    private readonly MvcProjContext _context;

    public StudentsController(MvcProjContext context)
    {
        _context = context;
    }
    public IActionResult GetStudents()
    {
        List<Student> students = _context.Student.ToList();
        return Json(students);
    }
    [HttpPost]
    public async Task<IActionResult> SaveStudents([FromBody] StudentChangesModel changes)
    {
        // Process added students
        foreach (var student in changes.AddedStudents)
        {
            _context.Add(student);
        }

        // Process deleted students
        foreach (var student in changes.DeletedStudents)
        {
            var data = await _context.Student.FindAsync(student.Id);

            _context.Student.Remove(data);
        }
        await _context.SaveChangesAsync();
        return Ok(new { message = "Changes saved successfully!" });
    }
}