No, you can't mine SWT. New SWT can only be minted by converting ARC tokens to SWT.
View the current total supply of SWT in circulation on Ethplorer here. The total number of SWT is equivalent to the ARC tokens that get converted into SWT. A total of 9,525,397.921984591306133876 ARC tokens were minted, so at most only 9,525,397 SWT can ever be minted.
Find more details in the Token Exchange Whitepaper.