The first pupil joined Year 11 at Stoke High School in September and is thought to be an asylum seeker.
One student at the school shared a photograph of him on Snapchat, commenting: “How’s there a 30-year-old man in our maths class.”
Now a second pupil, in Year 7, has also been removed from classes.
A spokesperson for the school said: “This is a matter for the Home Office and we have referred it to them.
“The student is not attending the school at this time. A student in Year 7 is also not currently attending school.
“We cannot comment further on individual cases but we have followed government and local authority policies and guidance, as we do for any admissions matter.”
The school added that parents had been informed and will be updated if there is any new information.
A Home Office spokesperson said: “We do not routinely comment on individual cases.”
If there is a doubt about someone’s age as part of an immigration case, the Home Office can arrange for social workers to undertake an age assessment.
The claimant must be treated as an adult if their physical appearance and demeanour “very strongly suggests that they are significantly over 18 years of age”.