This paper presents a multiwavelength study of the M8.0 flare and its associated fast halo CME that originated from a bipolar NOAA AR 10759 on 2005 May 13. The source active region has a conspicuous sigmoid structure at the TRACE 171 Å channel as well as in the SXI soft X-ray images, and we mainly concern ourselves with the detailed process of the sigmoid eruption, as evidenced by the multiwavelength data ranging from Hα, WL, EUV/UV, radio, and hard X-rays (HXRs). The most important finding is that the flare brightening starts in the core of the active region earlier than that of the rising motion of the flux rope. This timing clearly addresses one of the main issues in the magnetic eruption onset of sigmoid, namely, whether the eruption is initiated by an internal tether cutting to allow the flux rope to rise upward, or a flux rope rises due to a loss of equilibrium to later induce tether cutting below it. Our high time cadence SXI and Hα data show that the first scenario is relevant to this eruption. As in other major findings, we have the RHESSI HXR images showing a change of the HXR source from a confined footpoint structure to an elongated ribbon-like structure after the flare maximum, which we relate to the sigmoid-to-arcade evolution. The radio dynamic spectrum shows a type II precursor that occurred at the time of expansion of the sigmoid and a drifting pulsating structure in the flare rising phase in HXRs. Finally, type II and III bursts are seen at the time of maximum HXR emission, simultaneous with the maximum reconnection rate derived from the flare ribbon motion in UV. We interpret these various observed properties with the runaway tether-cutting model proposed by Moore et al. in 2001.