Normally we can apply the Copy feature and Paste feature to save filtered data into a new worksheet or workbook directly. You can do as follows:
1. Create a new worksheet with clicking the Add button  or  on the Sheet Tab bar.

Notes:
(1) Pressing Shift + F11 keys simultaneously can also create a new worksheet.
(2) If you are going to save the filtered data into a new workbook, just press Ctrl + N keys simultaneously to create a new workbook.

2. Select the filtered data, and copy it with pressing the Ctrl + C keys at the same time.

3. Go to the new worksheet or workbook, select a blank cell, and press Ctrl + V keys simultaneously to paste the filtered data.

Then you will see only filtered data are copied and pasted into the new worksheet/workbook. However, the row height and column width are lost. See below screen shots:

Easily split range based on criteria in a column and save split ranges to new new sheets

Kutools for Excel’s Split Data utility can help Excel users easily split a range to multiple worksheets based on criteria in one column of original range.

If the filtered data are too huge to select and copy easily, and you have customized column widths and row heights for many columns and rows, the Copying and Pasting may be not a good solution. In these conditions, you should try the Kutools for Excel's Delete Hidden (Visible) Rows & Columns utility.

1. Right click the sheet name which contains the filtered data in the Sheet Tab bar, and select the Move or Copy from the right-clicking menu.

Step 2: In the popping up Move or Copy dialog box, specify a workbook in the Move select sheets to book drop down list, check the Create a copy option, and click the OK button.

Note: To save filtered data into a new worksheet, select current workbook name in the Move Selected sheets To book drop down list; to save filtered data into a new workbook, please select (new book).

3. Now you will get into the new worksheet/workbook, please click the Kutools > Delete > Delete Hidden (Visible) Rows & Columns, and then in the opening dialog box,

(1) Select In Active Sheet in the Look in drop down list;
(2) Check Rows option in the Delete type section;
(3) Check Hidden Rows option in the Detailed type section;
(4) Click the Ok button.

It will take several minutes to delete all hidden rows if too many hidden rows exist. As deleting completes, a dialog bow will come out and tell you how many hidden rows have been deleted, just click Ok button to close it.

Now you will see all filtered data are reserved into the new worksheet, and all cell formatting including row heights and column widths are kept.

How to delete all hidden rows or columns in Excel?

How to delete hidden worksheets in Excel?