At this time the only way to clear a field resolution would be by adding a post-function in a workflow that does that as referred on the following article:

• Best practices on using the "Resolution" field

Nowadays, we can edit the resolution via REST API but we can't clear its value. It would be nice to have the option to clear the value via REST API.

Suggestion

"fields": {
    "resolution": { "name": "" }
}

Or even by simply setting as null.

"fields": {
     "resolution": null
}