How to export Sprout Form submissions with a JSON API endpoint?
Please see the Sprout Forms Element API documentation page. If it doesn't address your answer, please update your question and I can clarify further.

Here's the example from the docs of both a Form and Form Entries being retrieved from the Element API:

&lt;?php

use barrelstrength\sproutforms\elements\Form;
use barrelstrength\sproutforms\elements\Entry;

return [
    'endpoints' =&gt; [
        'api/sproutforms/&lt;formId:\d+&gt;.json' =&gt; function($formId) {
            return [
                'elementType' =&gt; Form::class,
                'criteria' =&gt; ['id' =&gt; $formId],
                'one' =&gt; true,
                'transformer' =&gt; function(Form $form) {
                    foreach ($form-&gt;getFieldLayout()-&gt;getTabs() as $tab) {
                        foreach ($tab-&gt;getFields() as $field) {
                            $fields[] = [
                                'field' =&gt; $field,
                                'folder' =&gt; $field-&gt;getFieldInputFolder()
                            ];
                        }

                        $tabs[] = [
                            'title' =&gt; $tab-&gt;name,
                            'fields' =&gt; $fields
                        ];
                    }

                    return [
                        'handle' =&gt; $form-&gt;handle,
                        'tabs' =&gt; $tabs
                    ];
                },
            ];
        },
        'api/sproutforms/&lt;formId:\d+&gt;/entries.json' =&gt; function($formId) {
            return [
                'elementType' =&gt; Entry::class,
                'criteria' =&gt; [
                    'formId' =&gt; $formId,
                    'status' =&gt; 'unread'
                ],
                'paginate' =&gt; true,
                'transformer' =&gt; function(Entry $entry) {
                    return [
                        'id' =&gt; $entry-&gt;id,
                        'dateCreated' =&gt; $entry-&gt;dateCreated,
                        'title' =&gt; $entry-&gt;title,
                        'customField' =&gt; $entry-&gt;customField,
                    ];
                },
            ];
        }
    ]
];