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The format in which you write down parameters in a launch file (or via rosparam) or even in a plain .yaml file is (as the filename implies): YAML.

YAML supports two notations for lists:

• on a single line: my_list: [a, b, c, d, .., z], and

• a more verbose formatting:

  my_list:
    - a
    - b
    - c
    - d
    - ..
    - z
  

No other forms are supported.

So:

How Can I read data in the format: [0.1 0.2 0.3] from the rosparameter server into a std::vector?

I would say "you can't", as what you show is not a valid notation for lists in YAML.

Perhaps it would be good / informative if you could explain why you would like to avoid commas.