Here is a simple Python implementation of a TODO list API:

```python
class TodoList:
    def __init__(self):
        self.todo_list = []

    def add_task(self, task):
        if not isinstance(task, str):
            raise ValueError("Task must be a string")
        self.todo_list.append(task)

    def remove_task(self, task):
        if task not in self.todo_list:
            raise ValueError("Task not found in the list")
        self.todo_list.remove(task)

    def get_tasks(self):
        return self.todo_list

    def update_task(self, old_task, new_task):
        if old_task not in self.todo_list:
            raise ValueError("Old task not found in the list")
        if not isinstance(new_task, str):
            raise ValueError("New task must be a string")
        index = self.todo_list.index(old_task)
        self.todo_list[index] = new_task

    def clear_list(self):
        self.todo_list = []
```

This API allows you to add tasks, remove tasks, get all tasks, update tasks, and clear the list. It also raises exceptions for invalid operations.

You can use this API like this:

```python
todo = TodoList()
todo.add_task("Buy groceries")
todo.add_task("Finish project")
print(todo.get_tasks())  # Output: ['Buy groceries', 'Finish project']
todo.update_task("Buy groceries", "Buy fruits")
print(todo.get_tasks())  # Output: ['Buy fruits', 'Finish project']
todo.remove_task("Finish project")
print(todo.get_tasks())  # Output: ['Buy fruits']
todo.clear_list()
print(todo.get_tasks())  # Output: []
```