Selección de filas de una tabla que tienen el mismo valor para un campo

Tendrás que unir a los estudiantes contra sí mismo:

SELECT s1.initials, s1.lastName
FROM Student s1, Student s2
WHERE s1.studentId <> s2.studentID /* Every student has the same tutor as himself */
AND s1.tutorId = s2.tutorid

Si desea generar los pares:

SELECT s1.initials, s1.lastName, s2.initials, s2.lastName
FROM Student s1, Student s2
WHERE s1.studentId <> s2.studentID /* Every student has the same tutor as himself */
AND s1.tutorId = s2.tutorid

Para obtener una lista de Tutor - Estudiantes:

SELECT tutorId, GROUP_CONCAT( initials, lastName SEPARATOR ', ') 
FROM `Student` 
GROUP BY tutorId
/* to only show tutors that have more than 1 student: */
/* HAVING COUNT(studentid) > 1 */