Sets in Mathematics are immutable but in Computer Science sets are mutable and called "Dynamic Sets" - truth of the statement
Set are at a higher level of abstraction than algorithms.  You can certainly analyze algorithms at that level of abstraction but that's not the usual level of abstraction for discussing algorithms, instead you'd refer to data structures such as stacks, vectors, lists, linked lists etc.
Sets are instead used in formal modeling contexts (Z,Coq,Agda,F-Star) to describe specifications but not algorithms.
They're also used do describe algorithms in functional programming (see e.g. Purely Functional Data Structures by Chris Okasaki ) but that is not very common in literature as most algorithms are described in terms of ephemeral data structures.
To answer your question, sets are the same both in Mathematics and CS, they're immutable.   Dynamic sets is a data structure loosely related to sets.
The author is not saying that sets are different in CS than in Mathematics.  He's saying that the data structures, as commonly described in algorithms are mutable.  CS is much more than algorithms and data structures.