Whether the king really did intend Roger's death, or if this was merely a rumour that found its way into several chronicles or was an invention to explain his dramatic escape and make it even more dramatic, is not clear; the Brut chronicle, somewhat implausibly, has Mortimer fleeing the day before his execution was due to be carried out. (This chronicle does include the detail that the constable Stephen Segrave and his men were given sedatives in their drink and says that they slept for two days and two nights while Mortimer escaped over the river Thames, though it gets the date of Mortimer's escape wrong by a week.)  Unfortunately, a leaf of the very well-informed Vita Edwardi Secundi is missing where the author might have discussed the escape. Adam Murimuth, a royal clerk and chronicler who must have come to know Mortimer well after 1326, says only that he escaped and fled to France and does not mention an impending execution.  The Scalacronica says only that he escaped; Lanercost says that Roger was "a baron of the king of England, who had fled from him previously to France to save his life", so evidently had heard the story of a possible execution; the Sempringham annalist does not mention an execution, stating correctly that Roger (oddly called 'Sir Roger Mortimer, the father') escaped on 1 August at night, crossed the Thames and fled to France; the Annales Paulini also does not mention an execution when describing Mortimer's escape.  The Anonimalle, a contination of the Brut which includes the story that Roger was to be executed, reports a rumour that Edward had sent letters declaring that Roger was due to have been drawn and hanged (traigne et pendu) a few days after his escape. 
1) The National Archives SC 8/6/255.
2) Calendar of Patent Rolls 1321-1324, p. 249. The judgement against the Mortimers is printed (in the original French) in James Conway Davies, The Baronial Opposition to Edward II: Its Character and Policy (1918), p. 565.
3) Calendar of Close Rolls 1323-1327, p. 13. This entry says that Segrave and "many others" in the Tower had been "poisoned by artifice."
4) Ibid., p. 132.
5) Patent Rolls 1321-1324, p. 335.
6) Close Rolls 1323-1327, p. 133.
7) Antonia Gransden, Historical Writing in England II: c. 1307 to the Early Sixteenth Century (1982), p. 20, citing Flores Historiarum, ed. H. R. Luard, vol. iii (1890), p. 217.
8) The Brut or the Chronicles of England, ed. F. W. D. Brie (1906), p. 231.
9) Adae Murimuth Continuatio Chronicarum, ed. E. M. Thompson (1889), p. 40.
10) Scalacronica: The Reigns of Edward I, Edward II and Edward III as Recorded by Sir Thomas Gray of Heton, knight, ed. Herbert Maxwell (1907) p. 72; The Chronicle of Lanercost 1272-1346, ed. Herbert Maxwell (1913), p. 251; Le Livere de Reis de Britanie e le Livere de Reis de Engletere, ed. John Glover (1865), p. 349; Annales Paulini 1307-1340 in W. Stubbs, ed., Chronicles of the Reigns of Edward I and Edward II, vol. 1 (1882), pp. 3-5-306.
11) The Anonimalle Chronicle 1307-41, from Brotherton Collection MS 29, ed. W. R. Childs and J. Taylor (1991), p. 116.
12) F.D. Blackley, 'Isabella and the Bishop of Exeter', in T.A. Sandqvist and M.R. Powicke, eds., Essays in Medieval History Presented to Bertie Wilkinson (1969), p. 221.