First, you need access to the WordPress database where WooCommerce stores its data. This is typically done through phpMyAdmin or any other database management tool that your hosting provider supports. Locate the database credentials, such as the database name, username, password, and host, from the wp-config.php file in your WordPress installation directory.

WooCommerce stores its data in several WordPress database tables. Key tables include `wp_posts` (for products), `wp_postmeta` (product details), `wp_woocommerce_order_items` (order items), and `wp_woocommerce_order_itemmeta` (order details). Identify and document the tables and fields you need for the data you want to move.

Use SQL queries to export the data from these tables. In phpMyAdmin, you can use the 'Export' feature to download the data in a format such as CSV or SQL. For example:
```sql
SELECT FROM wp_posts WHERE post_type = 'product';
```
Export the result set to a CSV file. Repeat this process for each relevant table.

Set up a MySQL database where you want to import the WooCommerce data. Use a tool like MySQL Workbench or the command line to create a new database and its relevant tables that mirror the structure of the WooCommerce tables. Make sure to create appropriate fields to accommodate your data.

Import the exported data into your MySQL destination. You can use the 'Import' feature in MySQL Workbench or phpMyAdmin to import CSV or SQL files. If importing CSV files, ensure your column mappings align with the destination schema. Use commands such as:
```sql
LOAD DATA INFILE 'path/to/your/file.csv'
INTO TABLE your_table
FIELDS TERMINATED BY ','
ENCLOSED BY '"'
LINES TERMINATED BY '\n'
IGNORE 1 ROWS;
```
Adjust the command parameters based on your CSV format.

After importing the data, verify its integrity by running SELECT queries to check if the data in the MySQL destination matches the data from WooCommerce. Look for any discrepancies or missing data and troubleshoot as needed. Ensure the data types and values are consistent with your expectations.

If you need to regularly update or synchronize data between WooCommerce and MySQL, consider automating the export and import processes using custom scripts. You can write a PHP or Python script that connects to the WooCommerce database, exports the data, and imports it into the MySQL destination on a scheduled basis using CRON jobs.

By following these steps, you can effectively move data from WooCommerce to a MySQL destination without relying on third-party connectors or integrations, ensuring you maintain control over your data transfer process.