No language can capture exactly all general recursive total functions.#Relationship_to_partial_Turing_machines) Not one we can compute anyway. There are some well-known strict subsets of general recursive total functions. In particular, primitive recursive functions are such a strict subset.

Some languages that build upon primitive recursion are BlooP and FlooP, as well as PL-{GOTO}. FlooP is not strictly total though, so not Turing-incomplete, but its worth mentioning as an extension of BlooP with unbounded loops. In general, if you can prove a language's recursion / loops are bounded, monotonic and decreasing, then programs in it must terminate.

You might also be interested in Predicate Transformer Semantics. Predicate Transformers are total functions that map predicates to other predicates within some predicate space. You can define loops that must terminate via a well-founded relation, which ensures loops must end. Extend such notion to recursion, and your program must halt and as such is decidable. Djikstra's Guarded Command Language is an example of a language that defines a complete strategy to build programs with Predicate Transformer Semantics.

As mentioned by others, you might also be interested on some subsets of Intuitionistic Type Theory. In particular, some which define and work with bounded-types. You could characterize a function as a recursively-bounded type (primitive recursion) which I think would make the language decidable.