We consider the properties of a self-avoiding polymer chain adsorbed on a solid attractive substrate which is attached with one end to a pulling force. The conformational properties of such chain and its phase behavior are treated within a grand canonical ensemble (GCE) approach. We derive theoretical expressions for the mean size of loops, trains, and tails of an adsorbed chain under pulling as well as values for the universal exponents which describe their probability distribution functions. A central result of the theoretical analysis is the derivation of an expression for the crossover exponent phi, characterizing polymer adsorption at criticality, phi = alpha - 1, which relates the precise value of phi to the exponent alpha, describing polymer loop statistics. We demonstrate that 1 - gamma(11) < alpha < 1 + nu, depending on the possibility of a single loop to interact with neighboring loops in the adsorbed polymer. The universal surface loop exponent gamma(11) approximate to -0.39 and the Flory exponent nu = 0.59. We present the adsorption-desorption phase diagram of a polymer chain under pulling and demonstrate that the relevant phase transformation becomes first order whereas in the absence of external force it is known to be a continuous one. The nature of this transformation turns to be dichotomic; i.e., coexistence of different phase states is not possible. These novel theoretical predictions are verified by means of extensive Monte Carlo simulations.