Silicon telluride (Si2Te3) is a two-dimensional material with a unique variable structure where the silicon atoms form Si-Si dimers to fill the "metal" sites between the Te layers. The Si-Si dimers have four possible orientations: three in-plane and one out-of-the plane directions. The structural variability of Si2Te3 allows unusual properties especially the mechanical properties. Using results from first-principles calculations, we show that the Si2Te3 monolayer can sustain a uniaxial tensile strain up to 38%, highest among all two-dimensional materials reported. The high mechanical flexibility allows applying mechanical strain to reduce the band gap by 1.4 eV. With increasing strain, the band gap undergoes an unusual indirect-direct-indirect-direct transition. We also show that the uniaxial strain can effectively control the Si-Si dimer alignment, which is beneficial for practical applications.