This work illustrates new tools and methods for an in vivo and direct, but non-invasive, measurement of an octopus arm mechanical properties. The active elongation (longitudinal stretch) and the pulling force capability are measured on a specimen of Octopus vulgaris in order to quantitatively characterize the parameters describing the arm mechanics, for biomimetic design purposes. The novel approach consists of observing and measuring a living octopus with minimally invasive methods, which allow the animal to move with its complete ability. All tools are conceived in order to create a collaborative interaction with the animal for the acquisition of active measures. The data analysis is executed taking into account the presence of an intrinsic error due to the mobility of the subject and the aquatic environment. Using a system of two synchronized high-speed high-resolution cameras and purpose-made instruments, the maximum elongation of an arm and its rest length (when all muscles fibres are relaxed during propulsion movement) are measured and compared to define the longitudinal stretch, with the impressive average result of 194%. With a similar setup integrated with a force sensor, the pulling force capability is measured as a function of grasp point position along the arm. The measured parameters are used as real specifications for the design of an octopus-like arm with a biomimetic approach.