I've seen several times people on the bench receiving yellow or red cards: substitutes, manager...
I wonder if a physio can be sent off, consequently he can't heal a player anymore.
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Team officials are cautioned and dismissed (receive yellow and red cards) (in law as of 2019-20) largely for inappropriate behaviour or interference with the game or mistreatment of other people.
There is no further specifications of who exactly can be a team official other than that they are, by definition,
[a]ny non-player listed on the official team list e.g. coach, physiotherapist, doctor (see technical staff)
Therefore, if a physio is included on the official team list and is not a player, they can be cautioned or dismissed for anything in Law 12.3 like any other team official.
If dismissed, this has the same consequences as it would for any person involved in the game. They
must leave the vicinity of the field of play and the technical area.
If they wish to treat a player or substitute or substituted player, that player must go to the physio - the physio cannot come to them on or near the field. Additional competition regulations may further disallow that involvement in the game or with the team and players.