Do you have permissions to edit alerts? Should be as easy as navigating to the card, either on the card/DataSet or Alerts in the top nav bar, then clicking share on the bottom of the alert, then expanding the already shared with section, then clicking the x on the far right on their name.

If you are talking automation, you can use the Product APIs for that. Authentication documentation: developer.domo.com/portal/8ba9aedad3679-ap-is#product-apis.

POST https://<instance>.domo.com/api/search/v1/query

Body:

{
    "count": 1000,
    "offset": 0,
    "combineResults": false,
    "query": "*",
    "filters": [
        {
            "name": "OWNED_BY_ID",
            "field": "owned_by_id",
            "facetType": "user",
            "value": "<user_id>:USER",
            "filterType": "term",
            "displayValue": "<user_name>",
            "translatedDisplayValue": "Owned by: <user_name>",
            "translatedPlaceHolderText": "Search people"
        }
    ],
    "sort": {
        "isRelevance": true
    },
    "facetValuesToInclude": [
        "TYPE"
    ],
    "facetValueLimit": 0,
    "facetValueOffset": 0,
    "includePhonetic": true,
    "queryProfile": "GLOBAL",
    "state": "list",
    "topic": null,
    "savedSearchId": null,
    "entityList": [
        [
            "alert"
        ]
    ]
}
 

Then loop through those results:
DELETE https://<instance>.domo.com/api/social/v4/alerts/<alert_id>/subscriptions?subscriberId=<user_id>&type=USER