Eclipse JEE Oxygen provides SourceMap debugging support (see bug 487465) with JSDT Debugger with classic Run / Debug as.

If you use Eclipse JEE Oxygen, you can run/debug TypeScript with Eclipse JEE Oxygen if *.js.map SourceMap files is generated.

The JSDT SourceMap debugging support is not perfect, but it starts working. Please create bugs at Eclipse bugzilla JSDT.

You can too install Webclipse which provides a debugger for TypeScript.